2nd Edition

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

**Also available as eBook on:**

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

Fuses

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

Transformers

Saturation of Current Transformers

Shunt Capacitors

Sub-Harmonic Frequencies

Static Power Converters

Switch-Mode Power (SMP) Supplies

Arc Furnaces

Cycloconverters

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

Inter-Harmonics

**Effects of Harmonics**

Rotating Machines

Transformers

Cables

Capacitors

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

Operation

Wind Generators

Power Electronics

Reactive Power Control

Harmonics

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

### Biography

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