1st Edition
Symmetrical Components for Power Systems Engineering
Emphasizing a practical conception of system unbalances, basic circuits, and calculations, this essential reference/text presents the foundations of symmetrical components with a review of per unit (percent), phasors, and polarity--keeping the mathematics as simple as possible throughout. According to IEEE Electrical Insulation Magazine, this book "…provides students and practicing engineers with a fundamental understanding of the method of symmetrical components and its applications in three-phase electrical systems. . .A useful feature of this book. . .is the incorporation of numerous examples in the text and 30 pages of problems."
Preface
Introduction and Historical Background
Introduction and General Aims
Historical Background
Per Unit and Percent Values
Introduction
Per Unit and Percent Definitions
Advantages of Per Unit and Percent
General Relationships Between Circuit Quantities
Base Quantities
Per Unit and Percent Impedance Relationships II
Per Unit and Percent Impedances of Transformer Units
Changing Per Unit (Percent) Quantities to Different Bases
Phasors, Polarity, and System Harmonics
Introduction
Phasors
Circuit and Phasor Diagrams for a Balanced Three-Phase Power System
Phasor and Phase Rotation
Polarity
Power System Harmonics
Basic Fundamentals and the Sequence Networks
Introduction
Positive-Sequence Set
Nomenclature Convenience
Negative-Sequence Set
Zero-Sequence Set
General Equations
Sequence Independence
Sequence Networks
Positive-Sequence Network
Negative-Sequence Network
Zero-Sequence Network
Impedance and Sequence Connections for Transformer Banks
Sequence Phase Shifts Through Wye-Delta Transformer Banks
Sequence Network Voltages
Sequence Network Reduction
Thevenin Theorem in Network Reduction
Wye-Delta Network Transformations
Short-Circuit MV A and Equivalent Impedance
Equivalent Network from a Previous Fault Study
Example: Determining an Equivalent Network from a Previous Fault Study
Network Reduction by Simultaneous Equations
Other Network Reduction Techniques
Shunt Unbalance Sequence Network Interconnections
Introduction
General Representation of Power Systems and Sequence Networks
Sequence Network Interconnections for Three- Phase Faults
Sequence Network Interconnections for Phaseto- Ground Faults
Sequence Network Interconnections for Phaseto- Phase Faults
Sequence Network Interconnections for Two- Phase-to-Ground Faults
Other Sequence Network Interconnections for Shunt System Conditions
Fault Impedance
Substation and Tower Footing Impedance
Ground Faults on Ungrounded or High Resistance Grounded Systems
Fault Calculation Examples for Shunt-Type Faults
Introduction
Faults on a Loop-Type Power System
Basic Assumptions
Fault Calculation
Summary of Fault Current
Voltages During Faults
Summary of Fault Voltages
Fault Calculations With and Without Load
Solution by Thevenin's Theorem
Solution by Network Reduction
Solution Without Load
Summary
Neutral Inversion
Example: Ground Fault on an Ungrounded System
Example: Ground Fault with High Resistance Across Three Distribution Transformers
Example: Ground Fault with High Resistance in Neutral
Example: Phase-a-to-Ground Fault Currents and Voltages on Both Sides of a Wye-Delta Transformer
Series and Simultaneous Unbalance Sequence Network Interconnections
Introduction
Series Unbalance Sequence Interconnections
One Phase Open: Broken Conductor or Blown Fuse .
Example: Open Phase Calculation
Simultaneous Unbalance Sequence Interconnections
Example: Broken Conductor Falling to Ground on Bus Side
Example: Broken Conductor Falling to Ground on Line Side
Example: Open Conductor on High Side and Ground Fault on Low Side of a Delta-Wye Transformer
Ground Fault on Low Side of a Delta-Wye Transformer
Example: Open Conductor on High Side and Ground Fault on Low Side of a Wye-Groundedl Delta-Wye-Grounded Transformer
Ground Fault Calculation for a Mid-Tapped Grounded Delta Secondary Transformer
Summary
Overview of Sequence Currents and Voltages During Faults
Introduction
Voltage and Current Phasors for Shunt Faults
System Voltage Profiles During Shunt Faults
Voltage and Current Phasors for All Combinations of the Four Shunt Faults
Summary
Transformer, Reactor, and Capacitor Characteristics
Transformer Fundamentals
Example: Impedances of Single-Phase Transformers in Three-Phase Power Systems
Polarity. Standard Terminal Marking, and Phase Shifts
Two-Winding Transformer Banks: Sequence Impedance and Connections
Three-Winding Transformer Banks
Three-Winding Transformers: Sequence Impedance and Connections
Example: Three-Winding Transformer Equivalent
Example: Three-Winding Transformer Fault Calculation
Autotransformers
Example: Autotransformer Fault Calculation
Ungrounded Autotransformers with Tertiary and Grounded Autotransformers Without Tertiary
Test Measurements for Transformer Impedance
Determination of the Equivalent Zero-Sequence Impedances for Three-Winding Three-Phase Transformers Where the Tertiary Delta Winding Is Not Available
Distribution Transformers with Tapped Secondary
Zig-Zag Connected Transformers
Reactors
Capacitors
Generator and Motor Characteristics
Introduction
Transient in Resistance-Inductance Series Circuits
Transient Generator Currents
Negative-Sequence Component
Zero-Sequence Component
Total RMS Armature Component
Rotating Machine Reactance Factors for Fault Calculations
Time Constants for Various Faults
Induction Machines
Summary
Appendix: Typical Constants of Three-Phase Synchronous Machines
Overhead Line Characteristics: Inductive Impedance
Introduction
Reactance of Overhead Conductors
GMR and GMD Values
The X" and Xd Line Constants
Positive- and Negative-Sequence Impedance
Example
Lines with Bundled Conductors
Zero-Sequence Impedance
Zero-Sequence Impedances of Various Lines
Summary for Zero-Sequence Impedance Calculations
Overhead Line Characteristics: Mutual Impedance
Introduction
Mutual Coupling Fundamentals
Positive- and Negative-Sequence Mutual Impedance
Zero-Sequence Mutual Impedance
Mutual Impedances Between Lines of Different Voltages
Power System-Induced Voltages in Wire Communication Lines
Summary
Overhead Line Characteristics: Capacitive Reactance
Introduction
Capacitance of Overhead Conductors
Positive- and Negative-Sequence Capacitance
Example: Three-Phase Circuit Capacitive Reactance
Example: Double-Three-Phase-Circuit Capacitive Reactance
Zero-Sequence Capacitance
Zero-Sequence Capacitance: Transposed Three- Phase Line
B Example: Zero-Sequence Capacitance, Transposed Three-Phase Line
Summary
Cable Characteristics
Introduction
Positive- and Negative-Sequence Constants
Three-Conductor Cables
Zero-Sequence Constants of Cables Problems
Appendix: Overhead Line Conductor Characteristics
Table A.I All-Aluminum Concentric-Lay Class AA and A Stranded Bare Conductors
Table A.2 All-Aluminum Concentric-Lay Class AA and A Bare Stranded Conductors 1350-H19 ASTM B 231
Table A.3 All-Aluminum Shaped-Wire Concentric-Lay Compact Conductors AAC/TW
Table A.4 All-Aluminum Shaped-Wire Concentric-Lay Compact Conductors AAC/TW
Table A.5 Bare Aluminum Conductors, Steel- Reinforced (ACSR) Electrical Properties of Single-Layer Sizes
Table A.6 Bare Aluminum Conductors, Steel- Reinforced (ACSR) Electrical Properties of Multilayer Sizes
Table A.7 Shaped-Wire Concentric-Lay Compact Aluminum Conductors Steel-Reinforced (ACSR/TW)
Table A.8 Shaped-Wire Concentric-Lay Compact Aluminum Conductors Steel-Reinforced (ACSR/TW) S
Table A.9 Bare Aluminum Conductors, - Wires Stranded with Aluminum-Clad Steel Wires (Alumoweld) as Reinforcement (A WAC) in Distribution and Neutral-Messenger Sizes
Bibliography
Index
Biography
Blackburn, J. Lewis
"…provides students and practicing engineers with a fundamental understanding of the method of symmetrical components and its applications in three-phase electrical systems. . .A useful feature of this book. . .is the incorporation of numerous examples in the text and 30 pages of problems. "
---IEEE Electrical Insulation Magazine