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