Clarke E. Circuit Analysis of A-C Power Systems, Volume I: Symmetrical and Related Components

John Wiley & Sons, 1943. — 540 p.This book is a compilation of notes and lectures given over a period of years to members of the Central Station Engineering Department of the General Electric Company in Schenectady, New York. Beginning in 1928, the notes were revised and extended for new groups of men entering the department, practical problems in power system performance with numerical solutions being added from time to time and they were presented by operating engineers. As the notes were helpful to members of the department and others receiving the, it was suggested that they be put in book form. In 1932, with Professor H. W. Bibber as co-author, a book on symmetrical components was undertaken. Parts of that unfinished book are included in Chapters I-IV of this one.In answer to the repeated request that the methods of symmetrical and related components be presented very simply, the methods of solving unbalanced power system problems by means of components are analyzed and discussed in detail. The book has been divided into two volumes. Volume I deals largely with the determination of currents and voltages of fundamental frequency in poor systems during unbalanced conditions by means of symmetrical and related components. included in this volume are the electrical characteristics of overhead transmission circuits and information and data on transformers and synchronous machines which permit them to be represented by equivalent circuits in the solution of practical problems. Volume II will give additional characteristics of synchronous machines, equivalent circuits for types of transformers not included in Volume I, characteristics of insulated cables, induction machines, and other electrical equipment encountered in a-c power systems. Overvoltages from various causes and the effects of saturation in transformers and of amortisseur windings in synchronous machines will also be included in Volume II. In both volumes special attention is given to equivalent circuits and the solutions of practical problems.Definitions and Fundamental Concepts
Vectors
Complex quantities
Operators
Vector representation of sinusoidal quantities
Conventions for current, voltage and power
Per cent and per unit quantities
Components
Superposition
Impedance networks
Self- and mutual impedances
Driving-point and transfer impedances
One-line diagram
Methods for deriving equivalent circuits
Two-, three-, and four-terminal equivalent circuits
Equivalent circuits for balanced three-phase systems
Three-phase faults
Symmetrical Components — Basic Equations for Three-Phase Systems
Short Circuits on Systems with One Power Source
Sequence impedances
Y-connected circuits
Δ-connected circuits
Sequence networks
Zero-sequence equivalent circuits for transformer banks
Shift in phase of positive- and negative-sequence components in Δ-Y transformer bank
Unsymmetrical Faults on Normally Balanced Three-Phase Systems
Short circuits
Faults replaced by equivalent circuits
Interconnections of sequence networks to represent faults
Faults through impedance
Open conductors
Two Component Networks for Three-Phase Systems
Positive-plus-negative, positive-minus-negative and zero-sequence components
Interconnection of component networks to represent unsymmetrical short circuits
Transmission Circuits with Distributed Constants
Equivalent circuits
Nominal T or Π
Equivalent T or Π
Hyperbolic functions from charts
Transmission line equations
Calculations involving capacitance
Ground-fault neutralizer
Fault voltages from charts
Equivalent circuits for two or more parallel transmission lines
Simultaneous Faults on Symmetrical Three-Phase Systems — Analysis by the Method of Symmetrical Components
Short circuits on grounded systems
Δ-Y transformer bank between faults
Ungrounded systems
Ground fault and open conductor
Unsymmetrical Three-Phase Circuits — Analysis by the Method of Symmetrical Components
Sequence impedances of the three phases
Sequence self- and mutual impedances of various types of circuits
Systems with unsymmetrical circuits
Solutions by means of equations
Faults treated as unsymmetrical circuits
Single-phase loads
Negative-sequence currents in rotating machines
Equivalent circuits
Open-Δ transformer bank
Transformer bank of dissimilar units
Sequence admittances
CHAPTER IX:Polyphase Systems of More than Three Phases, Single phase and Two-phase Systems
Symmetrical component equations for polyphase systems
Single phase systems treated as two-vector systems
Faults in three-wire single-phase systems
Two-phase systems
Positive- and negative sequence right-angle components
Positive- and zero-sequence symmetrical components
Phase quantities
Admittances of two-vector systems
Alpha, Beta, and Zero Components of Three-Phase Systems
α, β, 0 components defined in terms of phase quantities
History of α, β, 0 components
α and β generated voltages
α, β, 0 component networks
Relations between symmetrical components and α, β, 0 components
α, β, 0 self- and mutual impedances for various types of circuits
Equivalent circuits
Unsymmetrical circuits
Shift of α and β components in passing through Δ-Y transformer bank
Open-Δ transformer bank
Short circuits
Open conductors
Simultaneous dissymmetries
Scott-connected transformer bank
Interconnected three-phase and two-phase systems
Impedances of Overhead Transmission Lines
Self- and mutual impedances of parallel linear conductors
Sequence self- and mutual impedances of single-phase, two-phase, and three-phase circuits (earth neglected)
Carson’s formulas for earth-return circuits
Zero-sequence impedances
Reference for zero-sequence voltage
Zero-sequence reactance charts
Ground wires
Rails
Ground wire correction charts
Parallel transmission lines
Parallel circuits operated at different voltages
Zero-sequence currents in ungrounded loops
Positive- and negative-sequence self- and mutual impedances with ground wires (earth considered)
Three-phase circuit with neutral conductor
Single-phase and two-phase circuits. Rüdenberg’s equations
Zero-sequence equivalent circuits with impedance in earth-return path
Capacitances of Overhead Transmission Lines
Assumptions
Fundamental equations
Potential coefficients
Two methods for determining sequence capacitances
Maxwell’s coefficients
One-, two-, and three-conductor equivalent circuits in terms of Maxwell’s coefficients
Sequence capacitances from potential coefficients
Impedances versus admittances in calculations
60-cycle capacitive susceptance chart for three-phase circuits without ground wire
Three-phase circuits with ground wires
Ground wire correction charts
Parallel three-phase circuits, with and without ground wires
60-cycle zero-sequence mutual capacitive reactance chart
Single-phase and two-phase circuits
Appendix A: Determinants
Appendix B: Tables and Charts for Overhead Transmission Circuits
Solid, stranded, and hollow copper conductors
Aluminum cables, steel reinforced (ACSR)
Copperweld cables (30% and 40% conductivity) and Copperweld-copper cables
Iron and steel conductors
Rails
Positive-sequence reactance and capacitance charts
Corona starting voltage
Temperature-rise charts