2nd Edition

Power System Analysis Short-Circuit Load Flow and Harmonics, Second Edition

By J.C. Das Copyright 2012
    1092 Pages 479 B/W Illustrations
    by CRC Press

    1092 Pages 479 B/W Illustrations
    by CRC Press

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    Fundamental to the planning, design, and operating stages of any electrical engineering endeavor, power system analysis continues to be shaped by dramatic advances and improvements that reflect today’s changing energy needs. Highlighting the latest directions in the field, Power System Analysis: Short-Circuit Load Flow and Harmonics, Second Edition includes investigations into arc flash hazard analysis and its migration in electrical systems, as well as wind power generation and its integration into utility systems.

    Designed to illustrate the practical application of power system analysis to real-world problems, this book provides detailed descriptions and models of major electrical equipment, such as transformers, generators, motors, transmission lines, and power cables. With 22 chapters and 7 appendices that feature new figures and mathematical equations, coverage includes:

    • Short-circuit analyses, symmetrical components, unsymmetrical faults, and matrix methods
    • Rating structures of breakers
    • Current interruption in AC circuits, and short-circuiting of rotating machines
    • Calculations according to the new IEC and ANSI/IEEE standards and methodologies
    • Load flow, transmission lines and cables, and reactive power flow and control
    • Techniques of optimization, FACT controllers, three-phase load flow, and optimal power flow
    • A step-by-step guide to harmonic generation and related analyses, effects, limits, and mitigation, as well as new converter topologies and practical harmonic passive filter designs—with examples
    • More than 2000 equations and figures, as well as solved examples, cases studies, problems, and references

    Maintaining the structure, organization, and simplified language of the first edition, longtime power system engineer J.C. Das seamlessly melds coverage of theory and practical applications to explore the most commonly required short-circuit, load-flow, and harmonic analyses. This book requires only a beginning knowledge of the per-unit system, electrical circuits and machinery, and matrices, and it offers significant updates and additional information, enhancing technical content and presentation of subject matter. As an instructional tool for computer simulation, it uses numerous examples and problems to present new insights while making readers comfortable with procedure and methodology.

    Short-Circuit Currents and Symmetrical Components

    Nature of Short-Circuit Currents

    Symmetrical Components

    Eigenvalues and Eigenvectors

    Symmetrical Component Transformation

    Clarke Component Transformation

    Characteristics of Symmetrical Components

    Sequence Impedance of Network Components

    Computer Models of Sequence Networks

    Structure and Nature of Electrical Power Systems

    Power System Studies

    Unsymmetrical Fault Calculations

    Line-to-Ground Fault

    Line-to-Line Fault

    Double Line-to-Ground Fault

    Three-Phase Fault

    Phase Shift in Three-Phase Transformers

    Unsymmetrical Fault Calculations

    System Grounding

    Open Conductor Faults

    Matrix Methods for Network Solutions

    Network Models

    Bus Admittance Matrix

    Bus Impedance Matrix

    Loop Admittance and Impedance Matrices

    Graph Theory

    Bus Admittance and Impedance Matrices by Graph Approach

    Algorithms for Construction of Bus Impedance Matrix

    Short-Circuit Calculations with Bus Impedance Matrix

    Solution of Large Network Equations

    Current Interruption in AC Networks

    Rheostatic Breaker

    AC Arc Interruption

    Current-Zero Breaker

    Transient Recovery Voltage

    The Terminal Fault

    The Short-Line Fault

    Interruption of Low Inductive Currents

    Interruption of Capacitive Currents

    TRV in Capacitive and Inductive Circuits

    Prestrikes in Breakers

    Overvoltages on Energizing High-Voltage Lines

    Out-of-Phase Closing

    Resistance Switching

    Failure Modes of Circuit Breakers

    Operating Mechanisms-SF6 Breakers

    Vacuum Interruption

    Stresses in Circuit Breakers

    Application and Ratings of Circuit Breakers and Fuses according to ANSI Standards

    Total and Symmetrical Current Rating Basis

    Asymmetrical Ratings

    Voltage Range Factor K

    Circuit Breaker Timing Diagram

    Maximum Peak Current

    Permissible Tripping Delay

    Service Capability Duty Requirements and Reclosing Capability

    Capacitance Current Switching

    Line-Closing Switching Surge Factor

    Out-of-Phase Switching Current Rating

    Transient Recovery Voltage

    Generator Circuit Breakers

    Specifications of High-Voltage Circuit Breakers

    Low-Voltage Circuit Breakers


    Short Circuit of Synchronous and Induction Machines

    Reactances of a Synchronous Machine

    Saturation of Reactances

    Time Constants of Synchronous Machines

    Synchronous Machine Behavior on Terminal Short Circuit

    Circuit Equations of Unit Machines

    Park’s Transformation

    Park’s Voltage Equation

    Circuit Model of Synchronous Machines

    Calculation Procedure and Examples

    Short Circuit of Synchronous Motors and Condensers

    Induction Motors

    Short-Circuit Calculations according to ANSI Standards

    Types of Calculations

    Accounting for Short-Circuit Current Decay

    Rotating Machines Model

    Types and Severity of System Short Circuits

    Calculation Methods

    Network Reduction

    Breaker Duty Calculations

    Generator Source Short-Circuit Current Asymmetry

    Calculation Procedure

    Examples of Calculations

    Thirty-Cycle Short-Circuit Currents

    Short-Circuit Calculations According to IEC Standards

    Conceptual and Analytical Differences

    Prefault Voltage

    Far-from-Generator Faults

    Near-to-Generator Faults

    Influence of Motors

    Comparison with ANSI Calculation Procedures

    Examples of Calculations and Comparison with ANSI Methods

    Calculations of Short-Circuit Currents in DC Systems

    DC Short-Circuit Current Sources

    Calculation Procedures

    Short Circuit of a Lead Acid Battery

    Short-Circuit Current of DC Motors and Generators

    Short-Circuit Current of a Rectifier

    Short Circuit of a Charged Capacitor

    Total Short-Circuit Current

    DC Circuit Breakers

    Load Flow over Power Transmission Lines

    Power in AC Circuits

    Power Flow in a Nodal Branch

    ABCD Constants

    Transmission Line Models

    Tuned Power Line

    Ferranti Effect

    Symmetrical Line at No Load

    Illustrative Examples

    Circle Diagrams

    Modal Analysis

    Corona on Transmission Lines

    System Variables in Load Flow

    Load Flow Methods: Part I

    Modeling a Two-Winding Transformer

    Load Flow—Bus Types

    Gauss and Gauss–Seidel Y-Matrix Methods

    Convergence in Jacobi-Type Methods

    Gauss–Seidel Z-Matrix Method

    Conversion of Y to Z Matrix

    Triangular Factorization Method of Load Flow

    Load Flow Methods: Part II

    Function with One Variable

    Simultaneous Equations

    Rectangular Form of Newton–Raphson Method of Load Flow

    Polar Form of Jacobian Matrix

    Simplifications of Newton–Raphson Method

    Decoupled Newton–Raphson Method

    Fast Decoupled Load Flow

    Model of a Phase-Shifting Transformer

    DC Load Flow Models

    Second Order Load Flow

    Load Models

    Induction Motor Models

    Impact Loads and Motor Starting

    Practical Load Flow Studies

    Reactive Power Flow and Control

    Voltage Instability

    Reactive Power Compensation

    Reactive Power Control Devices

    Some Examples of Reactive Power Flow

    Flexible AC Transmission Systems

    Three-Phase and Distribution System Load Flow

    Phase Coordinate Method

    Three-Phase Models

    Distribution System Load Flow

    Optimal Capacitor Locations

    Optimization Techniques

    Functions of One Variable

    Concave and Convex Functions

    Taylor’s Theorem

    Lagrangian Method: Constrained Optimization

    Multiple Equality Constraints

    Optimal Load Sharing between Generators

    Inequality Constraints

    Kuhn–Tucker Theorem

    Search Methods

    Gradient Methods

    Linear Programming—Simplex Method

    Quadratic Programming

    Dynamic Programming

    Integer Programming

    Optimal Power Flow

    Optimal Power Flow

    Decoupling Real and Reactive OPF

    Solution Methods of OPF

    Generation Scheduling Considering Transmission Losses

    Steepest Gradient Method

    OPF Using the Newton Method

    Sequential Quadratic Programming

    Successive Linear Programming

    Interior Point Methods and Variants

    Security and Environmental Constrained OPF

    Harmonics Generation

    Harmonics and Sequence Components

    Increase in Nonlinear Loads

    Harmonic Factor

    Three-Phase Windings in Electrical Machines

    Tooth Ripples in Electrical Machines

    Synchronous Generators


    Saturation of Current Transformers

    Shunt Capacitors

    Sub-Harmonic Frequencies

    Static Power Converters

    Switch-Mode Power (SMP) Supplies

    Arc Furnaces


    Thyristor-Controlled Reactor

    Thyristor-Switched Capacitors

    Pulse-Width Modulation

    Adjustable Speed Drives

    Pulse Burst Modulation

    Chopper Circuits and Electric Traction

    Slip Frequency Recovery Schemes

    Lighting Ballasts

    Voltage Source Converters


    Effects of Harmonics

    Rotating Machines




    Harmonic Resonance

    Voltage Notching

    Electromagnetic Interference

    Overloading of Neutral

    Protective Relays and Meters

    Circuit Breakers and Fuses

    Telephone Influence Factor

    Harmonic Analysis

    Harmonic Analysis Methods

    Harmonic Modeling of System Components

    Load Models

    System Impedance

    Three-Phase Models

    Modeling of Networks

    Power Factor and Reactive Power

    Shunt Capacitor Bank Arrangements

    Unbalance Detection

    Study Cases

    Harmonic Mitigation and Filters

    Mitigation of Harmonics

    Band-Pass Filters

    Practical Filter Design

    Relations in an ST Filter

    Filters for a Furnace Installation

    Filters for an Industrial Distribution System

    Secondary Resonance

    Filter Reactors

    Double-Tuned Filter

    Damped Filters

    Design of a Second-Order High-Pass Filter

    Zero-Sequence Traps

    Limitations of Passive Filters

    Active Filters

    Corrections in Time Domain

    Corrections in the Frequency Domain

    Instantaneous Reactive Power

    Harmonic Mitigation AT Source

    Multilevel Converters

    Arc Flash Hazard Analysis

    Relating Short-Circuit Currents with Arc Flash and Personal Safety

    Arc Flash Hazard Analysis

    Hazard=Risk Categories

    System Grounding: Impact on Incident Energy

    Duration of an Arc Flash Event and Arc Flash Boundary

    Protective Relaying and Coordination

    Short-Circuit Currents

    Arc Flash Calculations in Medium-Voltage Systems

    Arc Flash Calculations in Low-Voltage Systems

    Accounting for Decaying Short-Circuit Currents

    Wind Power

    AEP 765 kV Transmission Grid Initiative in the United States

    Wind Energy Conversion

    The Cube Law


    Wind Generators

    Power Electronics

    Reactive Power Control


    Computer Modeling

    Appendix A: Matrix Methods

    Appendix B: Calculation of Line and Cable Constants

    Appendix C: Transformers and Reactors

    Appendix D: Sparsity and Optimal Ordering

    Appendix E: Fourier Analysis

    Appendix F: Limitation of Harmonics

    Appendix G: Estimating Line Harmonics


    J.C. Das is a consultant with Electrical Power Systems in Atlanta, Georgia.

    "The usefulness of this text comes from showing how to calculate and analyze many aspects of the power system without relying on a computer analysis. … [A] very useful text for an undergraduate or even graduate course in power engineering. … It would also make for a good reference book for practicing power system engineers."
    - IEEE Electrical Insulation Magazine, Vol. 20, No. 1, Jan/Feb 2004