1st Edition

Symmetrical Components for Power Systems Engineering

By J. Lewis Blackburn Copyright 1993

    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