Power System Protection

Cover
Title Page
Copyright
Contents
Author Biographies
Preface to the Second Edition
List of Symbols
Part I Protective Devices and Controls
Chapter 1 Introduction
1.1 Power System Protection
1.2 Prevention and Control of System Failure
1.2.1 Reactionary Devices
1.2.2 Safeguard Devices
1.2.3 Protective Device Operation
1.3 Protective System Design Considerations
1.4 Definitions Used in System Protection
1.5 System Disturbances
1.6 Book Contents
Problems
References
Chapter 2 Protection Measurements and Controls
2.1 Graphic Symbols and Device Identification
2.2 Typical Relay Connections
2.3 Circuit Breaker Control Circuits
2.4 Instrument Transformers
2.4.1 Instrument Transformer Selection
2.4.1.1 ANSI Standard CT Accuracy Classes
2.4.1.2 Excitation Curve Method
2.4.1.3 The Formula Method
2.4.1.4 The Simulation Method
2.4.2 Instrument Transformer Types and Connections
2.4.2.1 Conventional Current Transformers
2.4.2.2 Conventional Voltage (Potential) Transformers
2.4.2.3 Optical Current Transducers
2.4.2.4 Optical Voltage Transducers
2.5 Relay Control Configurations
2.6 Optical Communications
Problems
References
Chapter 3 Protective Device Characteristics
3.1 Introduction
3.2 Fuse Characteristics
3.2.1 Distribution Fuse Cutouts
3.2.2 Fuse Types
3.2.2.1 Standard Zero‐Current‐Clearing Fuses
3.2.2.2 Current Limiting Fuses
3.2.2.3 Special Fuses
3.2.2.4 Voltage Ratings
3.2.3 Fuse Time–Current Characteristics
3.2.4 Fuse Coordination Charts
3.3 Relay Characteristics
3.3.1 Relay Types
3.3.2 Electromechanical Relay Characteristics
3.3.3 Static Analog Relays
3.3.4 Differential Relays
3.3.5 Digital Relays
3.3.5.1 Historical Perspective of Digital Relaying
3.3.5.2 Digital Relay Configuration
3.3.5.3 The Substation Computer Hierarchy
3.3.5.4 Summary
3.3.6 Digital Overcurrent Relays
3.4 Power Circuit Breakers
3.4.1 Circuit Breaker Definitions
3.4.2 Circuit Breaker Ratings
3.4.3 Circuit Breaker Design
3.4.3.1 Circuit Breaker Fluids
3.4.3.2 Oil Circuit Breakers
3.4.3.3 Oilless Circuit Breakers
3.5 Automatic Circuit Reclosers
3.5.1 Recloser Ratings
3.5.2 Recloser Time–Current Characteristics
3.6 Automatic Line Sectionalizers
3.7 Circuit Switchers
3.8 Digital Fault Recorders
Problems
References
Chapter 4 Relay Logic
4.1 Introduction
4.2 Electromechanical Relay Logic
4.2.1 The Overcurrent Relay
4.2.2 The Distance Relay
4.3 Electronic Logic Circuits
4.3.1 Analog Logic Circuits
4.3.1.1 The Isolator
4.3.1.2 The Comparator or Level Detector
4.3.1.3 The Summer
4.3.1.4 The Integrator
4.3.1.5 Active Filters
4.3.1.6 Other Op Amp Applications
4.3.2 Digital Logic Circuits
4.3.2.1 Boolean Logic Circuits
4.3.2.2 The AND Logic
4.3.2.3 The OR Logic
4.3.2.4 The Exclusive OR Logic
4.3.2.5 The Buffer
4.3.2.6 The NOT or Negation Logic
4.3.2.7 The NOR Logic
4.3.2.8 The NAND Logic
4.3.2.9 The Time Delay Unit
4.3.2.10 The Flip‐Flop
4.3.2.11 Sampling of Analog Signals
4.3.2.12 The Analog‐to‐Digital (AID) Converter
4.4 Analog Relay Logic
4.4.1 An Instantaneous Overcurrent Relay
4.4.2 Phase Comparison Distance Relay
4.4.3 A Directional Comparison Pilot Relay
4.4.4 Conclusions Regarding Solid‐State Analog Logic
4.5 Digital Relay Logic
4.5.1 Digital Signal Processing
4.5.1.1 Linear Transformations
4.5.1.2 Frequency Response
4.5.1.3 Periodic Sequences
4.5.1.4 The Fast Fourier Transform
4.5.2 The Data Window Method
4.5.3 The Phasor Method
4.5.4 Digital Relaying Applications
4.5.4.1 Digital Overcurrent Protection
4.5.4.2 Digital Distance Relaying
4.5.4.3 Transformer Protection
4.5.4.4 Generator Protection
4.5.4.5 Digital Substation Protection
4.5.4.6 Other Types of Digital System Protection
4.5.4.7 Unique Concepts in Digital Protection
4.5.5 Example of a Digital Relay System
4.6 Hybrid Relay Logic
4.7 Relays as Comparators
4.7.1 Relay Design
4.7.2 Phase and Amplitude Comparison
4.7.3 The Alpha and Beta Planes
4.7.4 The General Comparator Equations
4.7.5 The Amplitude Comparator
4.7.6 The Phase Comparator
4.7.7 Distance Relays as Comparators
4.7.8 General Beta Plane Characteristics
Problems
References
Chapter 5 System Characteristics
5.1 Power System Faults
5.1.1 System Fault Characteristics
5.1.2 Fault Currents Near Synchronous Machines
5.1.3 Saturation of Current Transformers
5.2 Station Arrangements
5.2.1 Single Bus, Single Breaker Arrangement
5.2.2 Main and Transfer Arrangement
5.2.3 Double Bus, Single Breaker Arrangement
5.2.4 Double Bus, Double Breaker Arrangement
5.2.5 Ring Bus Arrangement
5.2.6 Breaker‐and‐a‐Half Arrangement
5.2.7 Other Switching Arrangements
5.2.7.1 Breaker and a Third Arrangement
5.2.7.2 The Ring Tripod Arrangement
5.2.7.3 The Ring Bridge Arrangement
5.2.7.4 The Crossed Ring Arrangement
5.2.7.5 The 4 × 6 Network Arrangement
5.2.7.6 The Pyramid Station Arrangement
5.3 Overhead Line Impedances
5.4 Computation of Available Fault Current
5.4.1 Three‐Phase (3PH) Faults
5.4.2 Double Line‐to‐Ground (2LG) Faults
5.4.3 Line‐to‐Line (LL) Fault
5.4.4 One‐Line‐to‐Ground (1LG) Fault
5.4.5 Summary of Fault Currents
5.5 System Equivalent for Protection Studies
5.5.1 The Open‐Circuit Impedance Matrix
5.5.2 Computation of the Two‐Port Representation
5.5.3 A Simple Two‐Port Equivalent
5.5.4 Tests of the Equivalent Circuit
5.5.5 System Equivalent from Two‐Port Parameters
5.5.6 Equivalent of a Line with Shunt Faults
5.5.7 Applications of the Equivalent to Series Faults
5.5.8 Conclusions Regarding Two‐Port Equivalents
5.5.9 Multiport Equivalents
5.5.9.1 The Two‐Port System Equivalent
5.5.9.2 The Three‐Port System Equivalent
5.5.9.3 The Four‐Port System Equivalent
5.6 The Compensation Theorem
5.6.1 Network Solution Before Changing Y3
5.6.2 Network Solution After Changing Y3
5.6.3 The Incremental Change in Current and Voltage
5.6.4 The Compensation Theorem in Fault Studies
5.7 Compensation Applications in Fault Studies
5.7.1 Prefault Conditions
5.7.2 The Faulted Network Condition
5.7.3 The Fault Conditions Without Load Currents
5.7.4 Summary of Load and Fault Conditions
Problems
References
Part II Protection Concepts
Chapter 6 Fault Protection of Radial Lines
6.1 Radial Distribution Systems
6.2 Radial Distribution Coordination
6.2.1 Supply System Information
6.2.2 Distribution Substation Information
6.2.3 Distribution System Information
6.2.4 Protective Equipment Information
6.2.5 Step‐by‐Step Study Procedure
6.3 Radial Line Fault Current Calculations
6.3.1 General Considerations for Radial Faults
6.3.2 Main Line Feeder Faults
6.3.2.1 Three‐Phase (3PH) Faults
6.3.2.2 Double Line‐to‐Ground (2LG) Faults
6.3.2.3 Line‐to‐Line (LL) Fault
6.3.2.4 One‐Line‐to‐Ground (1LG) Fault
6.3.2.5 Summary of Main Feeder Faults
6.3.3 Branch Line Faults
6.4 Radial System Protective Strategy
6.4.1 Clearing Temporary Faults
6.4.2 Isolating Permanent Faults
6.5 Coordination of Protective Devices
6.5.1 Recloser–Fuse Coordination
6.5.2 Recloser–Relay Coordination
6.6 Relay Coordination on Radial Lines
6.6.1 Coordination Procedure
6.6.2 Procedure for Phase and Ground Relays
6.6.3 Procedure for Instantaneous Relay Settings
6.7 Coordinating Protective Devices Measuring Different Parameters
6.7.1 Combined Time–Current Characteristics
6.7.2 Coordinating Time–Current Characteristics Across Transformers
6.7.3 Coordinating Two Overcurrent Relays Not Measuring the Same Currents
6.7.4 Time–Current Characteristics for Problem Solving
References
Chapter 7 Introduction to Transmission Protection
7.1 Introduction
7.2 Protection with Overcurrent Relays
7.2.1 Loops with One Current Source
7.2.2 Loops with Multiple Current Sources
7.3 Distance Protection of Lines
7.3.1 Distance Relay Characteristics
7.3.2 Zoned Distance Relays
7.3.3 Effect of Fault Resistance
7.3.3.1 Arc Resistance
7.3.3.2 Other Fault Resistance
7.3.4 Summary of Distance Relay Concepts
7.4 Unit Protection
7.5 Ground Fault Protection
7.5.1 Importance of Ground Fault Protection
7.5.2 Unique Characteristics of Ground Faults
7.5.3 Polarization of Ground Relays
7.5.3.1 Zero Sequence Voltage polarization
7.5.3.2 Negative Sequence Voltage Polarization
7.5.3.3 Zero Sequence Current Polarization
7.5.3.4 Dual (Zero Sequence) Polarizing
7.5.3.5 Negative and Zero Sequence Impedance
7.5.3.6 Virtual polarization
7.5.3.7 Voltage Compensation
7.5.4 Types of Ground Relays
7.6 Summary
Problems
References
Chapter 8 Complex Loci in the Z and Y Planes
8.1 The Inverse Z Transformation
8.2 Line and Circle Mapping
8.2.1 The Half Z Plane: a = c = 0
8.2.2 The Half Z Plane: R ≤ − k2
8.2.3 The Half Plane: a = b = 0
8.2.4 The Half Plane: a = 0
8.2.5 The Half Plane: d = 0
8.3 The Complex Equation of a Line
8.4 The Complex Equation of a Circle
8.5 Inversion of an Arbitrary Admittance
8.5.1 Inversion of Y with |YK| Constant and ψ Variable
8.5.2 Inversion of Y with ψ Constant and |YK| Variable
8.5.3 Summary of Y Inversion Equations
8.6 Inversion of a Straight Line Through (1, 0)
8.7 Inversion of an Arbitrary Straight Line
8.8 Inversion of a Circle with Center at (1, 0)
8.9 Inversion of an Arbitrary Circle
8.10 Summary of Line and Circle Inversions
8.11 Angle Preservation in Conformal Mapping
8.12 Orthogonal Trajectories
8.13 Impedance at the Relay
Problems
References
Chapter 9 Impedance at the Relay
9.1 The Relay Apparent Impedance, ZR
9.2 Protection Equivalent M Parameters
9.2.1 Network Test with EU Shorted
9.2.2 Network Test with ES Shorted
9.3 The Circle Loci Z = P/(1 ± YK)
9.4 ZR Loci Construction
9.4.1 k Circles
9.4.2 ψ Circles
9.5 Relay Apparent Impedance
9.5.1 The Unfaulted System
9.5.2 ABCD Parameters for a Faulted System
9.6 Relay Impedance for a Special Case
9.7 Construction of M Circles
9.7.1 Short‐Circuit Test with EU Shorted
9.7.2 Short‐Circuit Test with ES Shorted
9.7.3 Summary of Short‐Circuit Test Results
9.8 Phase Comparison Apparent Impedance
Problems
References
Chapter 10 Admittance at the Relay
10.1 Admittance Diagrams
10.2 Input Admittance Loci
10.2.1 YI Loci For Constant m
10.2.2 YI Loci for Constant ψ
10.3 The Relay Admittance Characteristic
10.4 Parallel Transmission Lines
10.5 Typical Admittance Plane Characteristics
10.6 Summary of Admittance Characteristics
Problems
Reference
Part III Transmission Protection
Chapter 11 Analysis of Distance Protection
11.1 Introduction
11.2 Analysis of Transmission Line Faults
11.2.1 Sequence Network Reduction
11.2.2 Phase Faults at F
11.2.2.1 Three‐Phase Faults
11.2.2.2 Phase‐to‐Phase Faults
11.2.3 Ground Faults at F
11.2.3.1 The One‐Line‐to‐Ground Fault at F
11.2.3.2 The Two‐Line‐to‐Ground Fault at F
11.3 Impedance at the Relay
11.3.1 Relay Impedances when C1 = C2
11.3.2 Apparent Relay Impedance Plots
11.4 Distance Relay Settings
11.5 Ground Distance Protection
11.6 Distance Relay Coordination
Problems
References
Chapter 12 Transmission Line Mutual Induction
12.1 Introduction
12.2 Line Impedances
12.2.1 Self‐ and Mutual Impedance
12.2.2 Estimation of Mutually Coupled Voltages
12.2.3 Example of Transmission Line Impedances
12.2.3.1 Self‐ and Mutual Impedances
12.2.3.2 Self‐ and Mutual Admittances
12.3 Effect of Mutual Coupling
12.3.1 Selecting a Reference Phasor
12.3.2 Transmission System Without Mutual Coupling
12.3.3 Transmission System with Mutual Coupling
12.3.4 Other Examples of Mutual Coupling
12.4 Short Transmission Line Equivalents
12.4.1 General Network Equivalents for Short Lines
12.4.2 Type 1 Networks
12.4.3 Type 2 Networks
12.4.4 Type 3 Networks
12.4.5 Lines with Appreciable Susceptance
12.4.6 Other Network Equivalents
12.5 Long Transmission Lines
12.5.1 The Isolated Long Transmission Line
12.5.2 Mutually Coupled Long Transmission Lines
12.5.2.1 Long Lines with Distinct Parameters
12.5.2.2 Long Lines with Identical Parameters
12.5.2.3 Representation of the Faulted Long Line
12.6 Long Transmission Line Equivalents
12.6.1 Reciprocity and the Admittance Matrix
12.6.2 The Long‐line Type 3 Network Equivalent
12.6.2.1 Type 3 Network Configuration
12.6.2.2 Type 3 Network in System Analysis
12.6.3 Long‐line Type 1 Network Equivalents
12.6.4 Long‐line Type 2 Network Equivalents
12.7 Solution of the Long‐line Case
12.7.1 Determination of the Sequence Impedances
12.7.2 Computation of Sequence Voltages and Currents
Problems
References
Chapter 13 Pilot Protection Systems
13.1 Introduction
13.2 Physical Systems for Pilot Protection
13.2.1 General Concepts of Pilot Communications
13.2.1.1 Signal Form
13.2.1.2 Signal Transmission Media
13.2.1.3 Performance Requirements for Protection Applications
13.2.2 Wire Pilot Systems
13.2.3 Power‐Line Carrier Pilot Systems
13.2.4 Microwave Pilot Systems
13.2.5 Fiber‐Optic Pilot Systems
13.2.6 Relay‐to‐Relay (Peer‐to‐Peer) Communications Systems
13.2.7 Guidelines for Pilot Communications Selection
13.2.8 Pilot Communications Problems
13.2.9 Pilot Protection Classifications
13.3 Non‐unit Pilot Protection Schemes
13.3.1 Directional Comparison Schemes
13.3.2 Distance Schemes
13.3.3 Transfer Trip Pilot Protection
13.3.3.1 Direct Underreaching Transfer Trip
13.3.3.2 Permissive Underreaching Transfer Trip
13.3.3.3 Permissive Overreaching Transfer Trip
13.3.3.4 Summary of Transfer Trip Schemes
13.3.4 Blocking and Unblocking Pilot Protection
13.3.4.1 Directional Comparison Blocking Scheme
13.3.4.2 Directional Comparison Unblocking
13.3.5 Selectivity in Directional Comparison Systems
13.3.6 Other Features of Directional Comparison
13.3.6.1 High‐Speed Reclosing
13.3.6.2 Power Swing Blocking
13.3.6.3 Ground Fault Protection
13.3.6.4 Switch‐onto‐Fault Function
13.3.7 Hybrid Schemes
13.4 Unit Protection Pilot Schemes
13.4.1 Phase Comparison Schemes
13.4.1.1 Single Phase‐Comparison Blocking
13.4.1.2 Dual Phase‐Comparison Unblocking
13.4.1.3 Segregated Phase Comparison
13.4.2 Line Current Differential Schemes
13.4.2.1 Wire Pilot Schemes
13.4.2.2 Differential Pilot Schemes
13.5 An Example of EHV Line Protection
13.5.1 Considerations in EHV Protection
13.5.2 Description of the EHV Pilot Protection
13.5.2.1 The PLC Pilot Protection System
13.5.2.2 The Microwave Pilot Protection System
13.5.2.3 Protection Equipment and Controls
13.6 Pilot Protection Settings
13.6.1 Instrument Transformer Settings
13.6.2 Characteristic (Maximum Torque) Angle
13.6.3 Distance Element Reach and Time Delay
13.6.3.1 Zone 1 Reach
13.6.3.2 Zone 2 Reach
13.6.3.3 Zone 3 Reach
13.6.3.4 Zone Element Time Delays
13.6.4 Phase Overcurrent Element Settings
13.6.4.1 Low‐Set Phase Overcurrent Elements
13.6.4.2 Medium‐Set Phase Overcurrent Elements
13.6.4.3 High‐Set Phase Overcurrent Elements
13.6.5 Residual Overcurrent Element Settings
13.6.6 Switch‐onto‐Fault Logic
13.6.7 Current Reversal Logic and Timers
13.6.8 Echo Keying
13.6.9 Weak Infeed Logic and Settings
13.6.10 Loss of Potential Logic
13.6.11 Conclusions Regarding Pilot Protection Settings
13.7 Traveling Wave Relays
13.8 Monitoring of Pilot Performance
Problems
References
Chapter 14 Complex Transmission Protection
14.1 Introduction
14.2 Single‐phase Switching of Extra‐high‐voltage Lines
14.2.1 Control of Secondary Arcs in Transposed Lines
14.2.2 Secondary Arcs in Untransposed EHV Lines
14.3 Protection of Multiterminal Lines
14.3.1 Distance Protection for a Three‐terminal Line
14.3.2 Pilot Protection for a Three‐terminal Line
14.3.2.1 Blocking Pilot Schemes
14.3.2.2 Transfer Trip Pilot Schemes
14.3.2.3 Line Current Differential Schemes
14.3.2.4 Summary of Pilot Relaying Schemes
14.4 Protection of Mutually Coupled Lines
14.4.1 Mutual Coupling of Parallel Lines
14.4.2 Ground Distance Protection of Type 1 Networks
14.4.2.1 Type 1 Distance Zones for Parallel Lines
14.4.2.2 Reach of the Relay at AR
14.4.2.3 Guidelines for the Underreaching Zone
14.4.2.4 Setting the Zone 1 Underreaching Relay
14.4.2.5 Guidelines for the Overreaching Zone
14.4.2.6 Zone 2 Impedance – Type 1.1 Configuration
14.4.2.7 Zone 2 Impedance – Type 1.3 Configuration
14.4.2.8 Computation of Relay AR Zone 2 Reach
14.4.2.9 Distance Measurement on Line B
14.4.3 Distance Protection of Type 2 Networks
14.4.4 Distance Protection of Type 3 Networks
Problems
References
Chapter 15 Series Compensated Line Protection
15.1 Introduction
15.1.1 The Degree of Compensation
15.1.2 Voltage Profile on Series Compensated Lines
15.2 Faults with Unbypassed Series Capacitors
15.2.1 End‐of‐Line Capacitors – Bus Side Voltage
15.2.2 End‐of‐Line Capacitors – Line Side Voltage
15.2.3 Capacitors at the Center of the Line
15.2.4 Conclusions on Series Compensation Effects
15.3 Series Capacitor Bank Protection
15.3.1 Series Capacitor Bypass Systems
15.3.1.1 Bypass Gaps
15.3.1.2 Metal Oxide Varistor Protection
15.3.1.3 Bypass Gap and Nonlinear Resistor
15.3.2 A Fundamental Frequency Varistor Model
15.3.3 Relay Quantities Including Varistor Bypass
15.3.4 Effect of System Parameters
15.3.4.1 Effect of Increased External Impedance
15.3.4.2 Effect of Increased Source Impedance
15.3.4.3 Effect of Increased Fault Impedance
15.4 Relay Problems Due to Compensation
15.4.1 The Effect of Transient Phenomena
15.4.2 The Effect of Phase Impedance Unbalance
15.4.3 Subsynchronous Resonance Effects
15.4.4 Voltage and Current Inversions
15.4.4.1 Midline Series Compensation
15.4.4.2 End‐of‐Line Series Compensation
15.4.4.3 Apparent Impedance Observations
15.4.5 Problems Due to Voltage Inversions
15.4.6 Problems Due to Mutual Induction
15.4.7 Problems in Reach Measurement
15.4.7.1 Underreaching Schemes
15.4.7.2 Overreaching Schemes
15.5 Protection of Series Compensated Lines
15.5.1 Line Current Differential and/or Current Phase Comparison
15.5.2 Directional Comparison Schemes
15.5.2.1 Hybrid Schemes
15.5.2.2 Distance Schemes
15.5.2.3 Traveling Wave Protection
15.5.3 Directional Overcurrent Ground Protection
15.6 Line Protection Experience
15.6.1 The Effect of Transient Phenomena on Protection
15.6.2 The Effect of Phase Impedance Unbalance
15.6.3 The Effect of Voltage and Current Inversions
15.6.4 The Effect of Fault Locator Error
15.6.5 The Effect of Transducer Error
15.6.6 Autoreclosing of Transmission Lines
15.6.7 Requirements for Protection System Studies
15.6.8 General Experience with Line Protection
Problems
References
Part IV Apparatus Protection
Chapter 16 Bus Protection
16.1 Introduction
16.2 Bus Configurations and Faults
16.3 Bus Protection Requirements
16.4 Bus Protection by Backup Line Relays
16.5 Bus Differential Protection
16.5.1 Current Transformers for Bus Protection
16.5.1.1 Bushing Current Transformers
16.5.1.2 Window‐Type Current Transformers
16.5.1.3 Wound‐Type Current Transformers
16.5.1.4 Auxiliary Current Transformers
16.5.1.5 Current Transformer Accuracy
16.5.1.6 Current Transformer Problems
16.5.2 Differential Protection Concepts and Problems
16.5.3 Differential Protection with Overcurrent Relays
16.5.4 Bus Protection with Percent Differential Relays
16.5.5 Bus Differential Protection with Linear Couplers
16.5.6 High‐Impedance Bus Differential Protection
16.6 Other Types of Bus Protection
16.6.1 Zone‐Interlocking/Blocking Bus Protection
16.6.2 Time‐Coordinated Overcurrent or Distance Protection
16.6.3 Fault Bus Protection
16.6.4 Combined Bus and Transformer Protection
16.6.5 Optical Arc Flash Bus Protection
16.6.6 Bus Protection Using Auxiliary CTs
16.6.6.1 Normal Conditions
16.6.6.2 External Fault with No Saturation
16.6.6.3 External Fault with CT Saturation
16.6.6.4 Internal Faults
16.6.6.5 Operating Characteristics
16.6.7 Directional Comparison Bus Protection
16.7 Auxiliary Tripping Relays
16.7.1 Lockout Relays (Function 86)
16.7.2 Nonlockout Relays (Function 94)
16.8 Summary
Problems
References
Chapter 17 Transformer and Reactor Protection
17.1 Introduction
17.2 Transformer Faults
17.2.1 External Faults
17.2.2 Internal Faults
17.2.2.1 Incipient Faults
17.2.2.2 Active Faults
17.2.3 Fault Protection Philosophy
17.3 Magnetizing Inrush
17.3.1 Magnetizing Current Magnitude
17.3.2 Magnetizing Inrush Current Harmonics
17.3.3 Sympathetic Inrush in Parallel Banks
17.4 Protection Against Incipient Faults
17.4.1 Protection Against External Incipient Faults
17.4.1.1 Overheating
17.4.1.2 Overfluxing
17.4.1.3 Other External Incipient Fault Conditions
17.4.2 Protection Against Internal Incipient Faults
17.5 Protection Against Active Faults
17.5.1 Connections for Differential Protection
17.5.1.1 Delta‐Wye Bank CT Connections
17.5.1.2 Current Transformer Ratios
17.5.2 Differential Protection of Transformers
17.5.2.1 Percent Slope of Differential Relays
17.5.2.2 Magnetizing Inrush Suppression
17.5.2.3 Three‐Winding Transformer Protection
17.5.2.4 Parallel Transformer Banks
17.5.2.5 Autotransformer Protection
17.5.2.6 Problems with Differential Relays
17.5.3 Overcurrent Protection of Transformers
17.5.4 Ground Fault Protection of Transformers
17.5.5 Transformer Protection Using Digital Multifunction Relays
17.6 Combined Line and Transformer Schemes
17.6.1 Nonunit Protection Schemes
17.6.1.1 Line Phase Fault Protection
17.6.1.2 Line Ground Fault Protection
17.6.2 Line and Transformer Unit Protection
17.7 Regulating Transformer Protection
17.8 Shunt Reactor Protection
17.8.1 Dry Type Reactors
17.8.2 Oil‐Immersed Reactors
17.8.2.1 Failure Modes of Shunt Reactors
17.8.2.2 Protection Practices for Shunt Reactors
17.9 Static Var Compensator Protection
17.9.1 A Typical SVC System
17.9.2 SVC Protection Requirements
Problems
References
Chapter 18 Generator Protection
18.1 Introduction
18.2 Generator System Configurations and Types of Protection
18.3 Stator Protection
18.3.1 Phase Fault Protection
18.3.2 Ground Fault Protection
18.3.2.1 Grounding Methods
18.3.2.2 Ground Fault Current Magnitude
18.3.3 Turn‐to‐Turn Fault Protection
18.3.4 Stator Open Circuit Protection
18.3.5 Overheating Protection
18.3.6 Overvoltage Protection
18.3.7 Unbalanced Current Protection
18.3.8 Backup Protection
18.4 Rotor Protection
18.4.1 Shorted Field Winding Protection
18.4.2 Grounded Field Winding
18.4.3 Open Field Winding
18.4.4 Overheating of the Field Winding
18.5 Loss of Excitation Protection
18.5.1 Operation as an Induction Generator
18.5.2 Loss of Field Protection
18.6 Other Generator Protection Systems
18.6.1 Overspeed Protection
18.6.2 Generator Motoring Protection
18.6.3 Vibration Protection
18.6.4 Bearing Failure Protection
18.6.5 Coolant Failure Protection
18.6.6 Fire Protection
18.6.7 Generator Voltage Transformer Fuse Blowing
18.6.8 Inadvertent Energizing
18.6.9 Protection of Power Plant Auxiliaries
18.7 Summary of Generator Protection
18.7.1 Unit Generator‐Transformer Protection
18.7.2 Unit Generator‐Transformer Trip Modes
18.7.3 Breaker Failure Protection of the Generator
Problems
References
Chapter 19 Motor Protection
19.1 Introduction
19.2 Induction Motor Analysis
19.2.1 Normalization of the Basic Equations
19.2.1.1 The Swing Equation
19.2.1.2 Normalization of the Swing Equation
19.2.1.3 Symmetrical Component Transformation
19.2.2 Induction Motor Equivalent Circuits
19.2.2.1 The Positive‐sequence Equivalent
19.2.2.2 The Negative‐sequence Equivalent
19.2.3 The Net Accelerating Torque
19.2.3.1 The Mechanical Torque
19.2.3.2 The Load Torque
19.2.3.3 The Accelerating Torque
19.2.3.4 The Swing Equation
19.2.3.5 Integration of the Swing Equation
19.2.4 Motor Electrical and Mechanical Performance
19.3 Induction Motor Heating
19.3.1 Heat Transfer Fundamentals
19.3.1.1 Heat Transfer by Conduction
19.3.1.2 Heat Transfer by Convection
19.3.1.3 Heat Transfer by Radiation
19.3.1.4 Heat Transfer Summary
19.3.2 A Motor Thermal Model
19.3.2.1 A Lumped‐parameter Model of the Motor
19.3.2.2 Thermal Model Parameters
19.3.2.3 Thermal Model Performance
19.3.2.4 Modeling Thermal Limits
19.3.2.5 Thermal Relay Realization
19.4 Motor Problems
19.4.1 Motor Problems Due to Internal Hazards
19.4.2 Motor Problems Due to External Hazards
19.4.2.1 Unbalanced Supply Voltage
19.4.2.2 Single Phasing of the Supply Voltage
19.4.2.3 Low Supply Voltage
19.4.2.4 Low System Frequency
19.4.2.5 Supply Voltage Reverse Phase Sequence
19.4.2.6 Motor Stalling Due to Excessive Load
19.4.2.7 Synchronous Motor Loss of Synchronism
19.4.2.8 Synchronous Motor Loss of Excitation
19.5 Classifications of Motors
19.5.1 Motors Classified by Service
19.5.1.1 Essential Service Motors
19.5.1.2 Nonessential Service Motors
19.5.2 Motors Classified by Location
19.5.3 Summary of Motor Classifications
19.6 Stator Protection
19.6.1 Phase Fault Protection
19.6.2 Ground Fault Protection
19.6.3 Locked Rotor Protection
19.6.4 Overload Protection
19.6.5 Undervoltage Protection
19.6.6 Reverse Phase Rotation Protection
19.6.7 Unbalanced Supply Voltage Protection
19.6.8 Loss of Synchronism in Synchronous Motors
19.6.9 Loss of Excitation in Synchronous Motors
19.6.10 Sudden Supply Restoration Protection
19.7 Rotor Protection
19.7.1 Rotor Heating
19.7.2 Rotor Protection Problems
19.8 Other Motor Protections
19.8.1 Bearing Protection
19.8.2 Complete Motor Protection
19.9 Summary of Large Motor Protections
Problems
References
Part V System Aspects of Protection
Chapter 20 Protection Against Abnormal System Frequency
20.1 Abnormal Frequency Operation
20.2 Effects of Frequency on the Generator
20.2.1 Overfrequency Effects
20.2.2 Underfrequency Effects
20.3 Frequency Effects on the Turbine
20.3.1 Overfrequency Effects
20.3.2 Underfrequency Effects
20.4 A System Frequency Response Model
20.4.1 Effect of Disturbance Size, Pstep
20.4.2 Normalization
20.4.3 Slope of the Frequency Response
20.4.4 The Effect of Governor Droop, R
20.4.5 The Effect of Inertia, H
20.4.6 The Effect of Reheat Time Constant, TR
20.4.7 The Effect of High‐Pressure Fraction, FH
20.4.8 The Effect of Damping, D
20.4.9 System Performance Analysis
20.4.10 Use of the SFR Model
20.4.11 Refinements in the SFR Model
20.4.11.1 Mechanical Power
20.4.11.2 Electrical Power
20.4.12 Other Frequency Response Models
20.4.13 Conclusions Regarding Frequency Behavior
20.5 Off Normal Frequency Protection
20.6 Steam Turbine Frequency Protection
20.7 Underfrequency Protection
20.7.1 A Typical Turbine Protection Characteristic
20.7.2 Load Shedding Traditional Relay Characteristics
20.7.2.1 Load Shedding Criteria
20.7.2.2 Definition of the Initial Load Imbalance
20.7.2.3 Load Shedding Protection Design
20.7.2.4 Turbine Protective Margin
20.7.3 Load Shedding Relay Connections
Problems
References
Chapter 21 Protective Schemes for Stability Enhancement
21.1 Introduction
21.2 Review of Stability Fundamentals
21.2.1 Definition of Stability
21.2.2 Power Flow Through an Impedance
21.2.3 Two‐Port Network Representation
21.2.4 The Swing Equation
21.3 System Transient Behavior
21.3.1 Stability Test System
21.3.2 Effect of Power Transfer
21.3.3 Effect of Circuit Breaker Speed
21.3.4 Effect of Reclosing
21.3.5 Relay Measurements During Transients
21.4 Automatic Reclosing
21.4.1 The Need for Fast (High Speed) Reclosing
21.4.2 Disturbance Considerations in Reclosing
21.4.2.1 Voltage Levels
21.4.2.2 Fault Types
21.4.3 Reclosing Considerations
21.4.3.1 Number of Reclosures
21.4.3.2 Reclosing Success
21.4.3.3 Definitions
21.4.3.4 Arc Deionization
21.4.4 Reclosing Relays
21.4.4.1 Breaker Operation
21.4.4.2 Single‐Shot Reclosing Relays
21.4.4.3 Multishot Reclosing Relays
21.4.4.4 Synchro‐Check Relays
21.4.4.5 Digital Reclosing and Synchronism Check Relay
21.4.5 Reclosing Switching Options
21.4.5.1 Single‐Phase Switching
21.4.5.2 Live Line, Dead Bus or Dead Line, Live Bus
21.4.5.3 Bus Protection Versus Line Protection
21.4.5.4 Delayed Autoreclosing
21.4.6 Reclosing at Generator Buses
21.5 Loss of Synchronism Protection
21.5.1 System Out‐of‐Step Performance
21.5.1.1 Representation in the Z Plane
21.5.1.2 Protection Requirements
21.5.2 Out‐of‐Step Detection
21.5.3 Out‐of‐Step Blocking and Tripping
21.5.4 Circuit Breaker Considerations
21.5.5 Pilot Relaying Considerations
21.5.5.1 Phase Comparison Pilot
21.5.5.2 Transfer Trip
21.5.5.3 Directional Comparison
21.5.6 Out‐of‐step Relaying Practice
21.6 Voltage Stability and Voltage Collapse
21.7 System Integrity Protection Schemes (SIPS)
21.7.1 SIPS Characteristics
21.7.2 Disturbance Events
21.7.3 SIPS Design Procedure
21.7.3.1 Definition of Critical Conditions
21.7.3.2 Definition of Recognition Triggers
21.7.3.3 Arming and Disarming Control of SIPS
21.7.4 Example of a System Integrity Protection Scheme
21.8 Summary
Problems
References
Chapter 22 Line Commutated Converter HVDC Protection
22.1 Introduction
22.2 LCC Dc Conversion Fundamentals
22.2.1 Rectifier Operation
22.2.1.1 Uncontrolled Six‐Pulse Rectifier Operation
22.2.1.2 The Controlled Rectifier
22.2.1.3 Normal Rectifier Operation with Commutation Overlap
22.2.2 Inverter Operation
22.2.3 Multibridge Converters
22.2.4 Characteristic LCC Converter Harmonics
22.2.5 Basic HVDC Control
22.3 Converter Station Design
22.3.1 A Typical Converter Station
22.3.2 HVDC Control Hierarchical Structure
22.3.3 General Philosophy of HVDC Protection
22.3.4 General Categories of HVDC Protection
22.4 Ac Side Protection
22.4.1 Ac Line Protection
22.4.2 Ac Bus Protection
22.4.3 Converter Transformer Protection
22.4.4 Filters and Reactive Support Protection
22.4.5 Generator Protection
22.5 Dc Side Protection Overview
22.5.1 Valve Protection
22.5.1.1 General Description of the Valves
22.5.1.2 Valve Short‐Circuit Protection
22.5.1.3 Converter Overcurrent Protection
22.5.1.4 Commutation Failure Protection
22.5.1.5 Valve Misfire Protection
22.5.1.6 Voltage Stress Protection
22.5.1.7 Excessive Delay Angle Protection
22.5.1.8 Dc Harmonics Protection
22.5.2 Other Dc Side Protective Functions
22.5.2.1 General Description
22.5.2.2 Converter Dc Differential Protection
22.5.2.3 Dc Line Protection
22.5.2.4 Dc Minimum Voltage Protection
22.5.2.5 Dc Overvoltage Protection
22.5.2.6 Pole Dc Differential Protection
22.5.2.7 Electrode Open‐Circuit Protection
22.5.2.8 Dc Filter Protection
22.5.2.9 Voltage‐Dependent Current‐Order Limit
22.6 Special HVDC Protections
22.6.1 General Description
22.6.2 Reverse Power Protection
22.6.3 Torsional Interaction Protection
22.6.4 Self‐Excitation Protection
22.6.5 Dynamic Overvoltage Protection
22.7 HVDC Protection Settings
22.8 Summary
Problems
References
Chapter 23 Voltage Source Converter HVDC Protection
23.1 Introduction
23.2 VSC HVDC Fundamentals
23.2.1 Voltage Source Converter Topologies
23.2.1.1 Two‐Level, Six‐Pulse Bridge VSC
23.2.1.2 Three‐Level Neutral Point Clamped VSC
23.2.1.3 Modular Multi‐Level Converters
23.2.2 VSC HVDC System Topologies
23.3 Converter Control Systems
23.3.1 Synchronization
23.3.2 Current Controllers
23.3.3 Outer Controllers
23.4 HVDC Response to Ac System Faults
23.5 Ac System Protection
23.5.1 Converter Station Ac Protection
23.5.1.1 Converter Station Ac Zone
23.5.1.2 Ac–Dc Connection Zone
23.5.1.3 Converter Protection Zone
23.5.2 Ac Line Protection
23.6 Dc Faults
23.6.1 Ac System Response to Dc Faults
23.6.2 Dc Protection Schemes
23.7 Multiterminal Systems
23.8 Hybrid LCC–VSC Systems
23.9 Summary
Problems
References
Chapter 24 Protection of Independent Power Producer Interconnections
24.1 Introduction
24.2 Renewable Resources
24.3 Transmission Interconnections
24.3.1 Interconnection Substations
24.3.1.1 Dedicated
24.3.1.2 Extended
24.3.2 Transmission Tapped Interconnections
24.3.2.1 Variety of Tapped Connections
24.3.2.2 Number and Length of Taps
24.3.2.3 Transient and Temporary Overvoltage Concerns
24.3.2.4 Ground Overcurrent Relay Desensitization
24.3.3 Transmission Interconnection Protection
24.3.3.1 Transmission Interconnection Line Protection
24.3.3.2 Special Considerations for IPP Transmission Interconnection Protection
24.4 Distribution Interconnections
24.4.1 Distributed Resource Size
24.4.2 Dedicated Interconnection Feeders
24.4.2.1 Protection Modifications Required
24.4.3 Shared Interconnection Feeders
24.4.3.1 Protection Concerns
24.5 Summary
Problems
References
Chapter 25 SSR and SSCI Protection
25.1 Introduction
25.2 SSR Overview
25.2.1 Types of SSR Interactions
25.2.1.1 Induction Generator Effect
25.2.1.2 Torsional Interaction
25.2.1.3 Transient Torques
25.2.2 A Brief History of SSR Phenomena
25.3 SSR and SSCI System Countermeasures
25.3.1 Network and Source Controls
25.3.1.1 System Switching
25.3.1.2 Series Capacitor Voltage Control
25.3.1.3 Thyristor‐controlled Series Capacitors
25.3.1.4 Power Converter Control Modifications
25.3.1.5 Unit Tripping
25.3.2 Generator and System Modifications
25.3.2.1 Turbine‐generator Modifications
25.3.2.2 Generator Circuit Series Reactance
25.4 SSR Source Countermeasures
25.4.1 Filtering and Damping
25.4.1.1 Static Blocking Filters
25.4.1.2 Line Filters
25.4.1.3 Dynamic Filters
25.4.1.4 Dynamic Stabilizers
25.4.1.5 Excitation System Dampers
25.4.2 Relay Protection and Monitoring
25.4.2.1 SSR Protective Relays
25.4.2.2 SSR Monitors
25.4.2.3 Comments on SSR Relays
25.5 Summary
Problems
References
Part VI Reliability of Protective Systems
Chapter 26 Basic Reliability Concepts
26.1 Introduction
26.2 Probability Fundamentals
26.2.1 The Probability Axioms
26.2.1.1 Frequency Interpretation
26.2.2 Events and Experiments
26.2.3 Venn Diagrams
26.2.3.1 Union of Events
26.2.3.2 Intersection of Events
26.2.4 Classes and Partitions
26.2.5 Rules for Combining Probabilities
26.2.5.1 Rule 1 – Independent Events
26.2.5.2 Rule 2 – Mutually Exclusive Events
26.2.5.3 Rule 3 – Complementary Events
26.2.5.4 Rule 4 – Conditional Events
26.2.5.5 Rule 5 – Simultaneous Events
26.2.5.6 Rule 6 – Occurrence of One of Two Events
26.2.5.7 Rule 7 – Conditional Probability
26.3 Random Variables
26.3.1 Definition of a Random Variable
26.3.2 The Cumulative Probability Distribution Function
26.3.3 The Probability Density Function
26.3.4 Discrete Distributions
26.3.5 Continuous Distributions
26.3.6 Moments
26.3.7 Common Probability Distribution Functions
26.3.7.1 Discrete Distributions
26.3.7.2 Continuous Distributions
26.3.8 Random Vectors
26.3.9 Stochastic Processes
26.3.10 Power System Disturbances
26.4 Failure Definitions and Failure Modes
26.4.1 Failure Definitions
26.4.2 Modes of Failure
26.5 Reliability Models
26.5.1 Definition of Reliability
26.5.1.1 The Failure Process
26.5.1.2 The Hazard Rate
26.5.1.3 The Mean Time to Failure
26.5.2 The Repair Process
26.5.2.1 Ideal Repair
26.5.2.2 Repair and Preventive Maintenance
26.5.2.3 Probabilistic Repair Parameters
26.5.3 The Whole Process
26.5.3.1 The Conditional Failure Intensity
26.5.3.2 The Unconditional Failure Intensity
26.5.3.3 The Expected Number of Failures
26.5.3.4 The Conditional Repair Intensity
26.5.3.5 The Unconditional Repair Intensity
26.5.3.6 The Expected Number of Repairs
26.5.3.7 The Mean Time Between Failures
26.5.3.8 Summary of Whole Process Variables
26.5.4 Constant Failure and Repair Rate Model
Problems
References
Chapter 27 Reliability Analysis
27.1 Reliability Block Diagrams
27.1.1 Series Systems
27.1.2 Parallel Systems
27.1.3 Series–Parallel and Parallel–Series Systems
27.1.4 Standby Systems
27.1.5 Bridge Networks
27.1.6 Cut Sets
27.2 Fault Trees
27.2.1 Fault Tree Conventions
27.2.2 System Analysis Methods
27.2.3 System Components
27.2.4 Component Failures
27.2.5 Basic Fault Tree Construction
27.2.6 Decision Tables
27.2.7 Signal Flow Graphs
27.3 Reliability Evaluation
27.3.1 Qualitative Analysis
27.3.1.1 Cut Sets
27.3.1.2 Qualitative Importance
27.3.1.3 Common Mode Failure Analysis
27.3.1.4 Other Qualitative Methods
27.3.2 Quantitative Analysis
27.3.2.1 Top Event Analysis
27.3.2.2 Boolean Algebra
27.3.2.3 Availability and Unavailability
27.3.2.4 Quantitative Importance
27.3.2.5 Top Event Prevention
27.4 Other Analytical Methods
27.4.1 Reliability Block Diagrams
27.4.2 Success Trees
27.4.3 Truth Tables
27.4.4 Structure Functions
27.4.5 Minimal Cut Sets
27.4.6 Minimal Path Sets
27.5 State Space and Markov Processes
27.5.1 The Markov Process
27.5.2 Stationary State Probabilities
27.5.3 General Algorithm for Markov Analysis
27.5.4 Model of Two Repairable Components
27.5.5 Markov Models with Special Failure Modes
27.5.6 Failure Frequency and Duration
Problems
References
Chapter 28 Reliability Concepts in System Protection
28.1 Introduction
28.2 System Disturbance Models
28.2.1 A Probabilistic Disturbance Model
28.2.2 Disturbance Distribution
28.2.3 Disturbance Classifications
28.2.4 Probabilistic Model of Disturbances
28.2.5 Disturbance Joint Probability Density
28.3 Time‐Independent Reliability Models
28.3.1 The Protection and the Protected Component
28.3.2 System Reliability Concepts
28.3.2.1 Dual Failure Modes of Protective Systems
28.3.2.2 Operational Failure (Fail Dangerous)
28.3.2.3 Security Failure (Fail Safe)
28.3.2.4 Optimization
28.3.2.5 Dual Redundant Systems
28.3.2.6 Fault Tree Analysis
28.3.3 Coherent Protection Logic
28.3.3.1 Two‐Relay Systems
28.3.3.2 Three‐Relay Systems
28.3.3.3 Analysis of Coherent Systems
28.3.4 Protective System Analysis
28.3.4.1 Protective System
28.3.4.2 Total System Operational Failure
28.3.4.3 Block Diagrams of Operational Failure
28.3.4.4 Block Diagrams of Security Failure
28.3.5 Specifications for Transmission Protection
28.3.5.1 Relay Specifications
28.3.5.2 Switching Station Specifications
28.3.5.3 Communications Specifications
28.4 Time‐Dependent Reliability Models
28.4.1 Failure Distributions of Random Variables
28.4.1.1 Series Connection of A and B
28.4.1.2 Parallel Connection of A and B
28.4.1.3 Standby Redundancy
28.4.1.4 Sequential Operation
28.4.2 Composite Protection System
28.4.2.1 The Main Protection System
28.4.2.2 Random Time Evaluation
Problems
References
Chapter 29 Fault Tree Analysis of Protective Systems
29.1 Introduction
29.2 Fault Tree Analysis
29.2.1 System Nomenclature
29.2.2 Calculation of Component Parameters
29.2.2.1 Component Unconditional Intensities
29.2.2.2 Expected Number of Failures and Repairs
29.2.2.3 Component Unavailability
29.2.2.4 Component Conditional Intensities
29.2.3 Computation of Minimal Cut Set Parameters
29.2.3.1 Cut Set Unavailabilities
29.2.3.2 Conditional and Unconditional Intensities
29.2.3.3 Expected Number of Failures and Repairs
29.2.4 Computation of System Parameters
29.2.4.1 System Unavailability
29.2.4.2 System Unconditional Intensities
29.2.4.3 Other System Parameters
29.2.4.4 Short Cut Methods
29.3 Analysis of Transmission Protection
29.3.1 Functional Specification for the Protective System
29.3.2 The Top Event
29.3.3 Failure of the Circuit Breakers
29.3.4 Protective System Failure
29.3.4.1 Modes of Pilot Signaling
29.3.4.2 Transmitter and Receiver Modeling
29.3.4.3 Communication Links
29.3.4.4 Failure to Clear Left End Zone 1 Faults
29.3.4.5 Failure to Clear Right‐End Zone 1 Faults
29.3.4.6 Failure to Clear Midline Zone 1 Faults
29.4 Fault Tree Evaluation
29.4.1 Breaker Failure Evaluation
29.4.2 Protective System Failure Evaluation
29.4.2.1 Failure to Clear Left End Zone 1 Faults
29.4.2.2 Failure to Clear Right End Zone 1 Faults
29.4.2.3 Failure to Mid‐Line Zone 1 Faults
29.4.3 Determination of Minimal Cut Sets
29.4.4 Constant Failure Rate‐Special Cases
29.4.4.1 Monitored Systems
29.4.4.2 Periodically Test Systems
Problems
References
Chapter 30 Markov Modeling of Protective Systems
30.1 Introduction
30.2 Testing of Protective Systems
30.2.1 The Need for Testing
30.2.2 Reliability Modeling of Inspection
30.3 Modeling of Inspected Systems
30.3.1 Optimal Inspection Interval
30.3.2 Optimization for Redundant Systems
30.3.3 Optimal Design of k‐out‐of‐n:G Systems
30.3.3.1 Assumptions
30.3.3.2 Probability of FD Failures
30.3.3.3 Probability of FS Failures
30.3.3.4 Optimization
30.4 Monitoring and Self‐testing
30.4.1 Monitoring Techniques
30.4.2 Self‐Checking Techniques
30.4.3 Monitoring and Self‐Checking Systems
30.4.4 Automated Testing
30.4.5 Intelligent Monitoring and Testing
30.5 The Unreadiness Probability
30.6 Protection Abnormal Unavailability
30.6.1 Assumptions
30.7 Evaluation of Safeguard Systems
30.7.1 Definitions and Assumptions
30.7.2 The Unconditional Hazard Rate
30.7.3 Expected Number of Failures
Problems
References
Appendix A Protection Terminology
A.1 Protection Terms and Definitions
A.2 Relay Terms and Definitions
A.3 Classification of Relay Systems
A.4 Circuit Breaker Terms and Definitions
References
Appendix B Protective Device Classification
B.1 Device Function Numbers
B.2 Devices Performing More than One Function
B.2.1 Suffix Numbers
B.2.2 Suffix Letters
B.2.3 Representation of Device Contacts on Electrical Diagrams
Appendix C Overhead Line Impedances
Appendix D Transformer Data
Appendix E 500 kV Transmission Line Data
E.1 Tower Design
E.2 Unit Length Electrical Characteristics
E.3 Total Line Impedance and Admittance
E.4 Nominal Pi
E.5 ABCD Parameters
E.6 Equivalent Pi
E.7 Surge Impedance Loading
E.8 Normalization
E.9 Line Ratings and Operating Limits
References
Index
EULA