Power systems applications of graph theory / Jizhong Zhu.

Format:

Book

Author/Creator:

Zhu, Jizhong, 1961-

Series:

Energy science, engineering and technology series.

Energy science, engineering and technology series

Language:

English

Subjects (All):

Electric power systems--Mathematical models.

Electric power distribution--Mathematical models.

Graph theory.

System analysis.

Physical Description:

1 online resource (334 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, c2009.

Language Note:

English

Summary:

This book attempts to cover all applications of graph theory in the area of power systems. Consisting of two parts, it first introduces the basic concepts of graph theory and then describes the practical application of graph theory and network flow programming to all kinds of power systems problems.

Contents:

Intro

POWER SYSTEMS APPLICATIONS OF GRAPH THEORY

LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA

CONTENTS

PREFACE

Chapter 1: Introduction

REFERENCES

Chapter 2: Basic Concepts of Graph

2.1. INTRODUCTION

2.2. BASIC CONCEPTS

2.3. BASIC STRUCTURAL PROPERTIES

Chapter 3: Graph Theory

3.1. INTRODUCTION

3.2. LINEAR ALGEBRA RELATED TO GRAPH THEORY

3.3. CONNECTIVITY

3.4. TREES

3.4.1. Properties of Tree

3.4.2. Optimal Tree

3.5. COLORING

3.5.1. Edge Coloring

3.5.2. Vertex Coloring

3.6. THE SHORTEST PATH PROBLEM

3.6.1. Dijkstra's Algorithm

3.6.2. A* Search Algorithm

3.7. PLANAR GRAPHS

3.7.1. Planar Graph and Dual Graph

3.7.2. Euler's Formula

3.8. MATROID THEORY

3.8.1. Matroids

3.8.2. Matroid Theory and Extensions

3.8.3. Basic Constructions of Matroid

3.8.4. Weighted Matroid

Chapter 4: Network Flow Programming

4.1. NETWORK

1. Capacity Constraints

2. Skew Symmetry

3. Flow Conservation

4.2. MAXIMUM FLOW PROBLEM

4.2.1. Max-Flow Min-Cut Theorem

4.2.2. Ford-Fulkerson Algorithm

4.2.3. Push-Relabel Algorithm

4.2.4. Linear Programming Applied to Max-Flow

4.3. Minimum Cost Flow Problem

4.3.1. Description of the Problem

4.3.2. Working with Residual Networks

4.3.3. Cycle-Canceling Algorithm

4.3.4. Successive Shortest Path Algorithm

4.3.5. Primal-Dual Algorithm

4.4. MINIMUM SPANNING TREE

4.4.1. Prim's Algorithm

4.4.2. Euclidean Minimum Spanning Tree

4.5. THE TRANSPORTATION PROBLEM

Chapter 5: Power Flow and Network Flow

5.1. INTRODUCTION

5.2. MATHEMATICAL MODEL OF POWER SYSTEM

5.3. NEWTON-RAPHSON METHOD

5.3.1. Principle of Newton Raphson Method

5.3.2. Power Flow Solution with Polar Coordinate System.

5.4. P-Q DECOUPLING METHOD

5.5. DC POWER FLOW

5.6. NETWORK FLOW

Chapter 6: Minimum Cost Flow Method for Power Systems Economic Dispatch

6.1. INTRODUCTION

6.2. CLASSICAL ECONOMIC DISPATCH METHOD

6.2.1. Input-Output Characteristic of Thermal Units

6.2.2. Equal Incremental Principle

6.3. MINIMUM COST FLOW DISPATCH METHOD

6.4. HYDRO-THERMAL SYSTEM ECONOMIC DISPATCH

6.4.1. Input-Output Characteristic of Hydroelectric Units

6.4.2. Hydro-Thermal System Economic Dispatch

6.4.3. Numerical Example

Chapter 7: Application of Out-of-Kilter Algorithm to Economic Power Dispatch

7.1. INTRODUCTION

7.2. OUT-OF-KILTER ALGORITHM

7.2.1. OKA Model

7.2.2. Complementary Slackness Conditions for Optimality of OKA

7.2.3. Labeling Rules and Algorithm of OKA

7.3. N SECURITY ECONOMIC DISPATCH MODEL

7.4. CALCULATION OF N - 1 SECURITY CONSTRAINTS

7.5. N - 1 SECURITY ECONOMIC DISPATCH

7.6. SIMULATIONS

7.6.1. Major procedures of the OKA

7.6.2. Numerical Examples

APPENDIX A. IEEE 5 BUS SYSTEM

APPENDIX B. IEEE 30 BUS SYSTEM

Chapter 8: Application of Graph Theory to Power Systems State Estimation

8.1. INTRODUCTION

8.2. TOPOLOGICAL OBSERVABILITY ANALYSIS

8.2.1. Formulation of Topological Observability

8.2.2. Illustration

8.2.3. Augmented Graph for Observability Analysis

8.3. IDENTIFICATION OF BAD MEASUREMENT DATA

8.3.1. Properties and Classification of Bad Data Groups

8.3.2. Criticality of Flow Measurements Based on Graph Theory

Chapter 9: Application of Nonlinear Convex Network Flow Programming to Multi-Area System Economic Dispatch

9.1. INTRODUCTION

9.2. NLCNFP MODEL OF MAED

9.2.1. Traditional ED Model

9.2.2. Consideration of KVL

9.2.3. MAED Model

9.3. NLCNFP ALGORITHM

9.4. SIMULATIONS

REFERENCES.

Chapter 10: Secure and Economic Automatic Generation Control

10.1. INTRODUCTION

10.2. NLCNFP MODEL OF EDC

10.2.1. Mathematical Model

10.2.2. Consideration of KVL

10.3. INCREMENTAL NLCNFP MODEL OF AGC

10.4. THE SOLUTION METHOD

10.5. NUMERICAL EXAMPLE

Chapter 11: VAR Optimization and Pricing in Multi-Area Power System

11.1. INTRODUCTION

11.2. OPTIMAL MODEL IN MULTI-AREAS

1. Objective Function

2. Constraints

11.3. VAR PRICING IN MULTI-AREAS

11.4. SELECTION OF VAR SOURCES

11.5. TEST RESULTS AND ANALYSIS

11.6. CONCLUSION

Chapter 12: Automatic Contingency Selection and Ranking

12.1. INTRODUCTION

12.2. PERFORMANCE INDEX

12.3. MATHEMATICAL MODEL

12.3.1. Real Power Network Model

12.3.2. Reactive Power Network Model

12.3.3. Unified NFP Model for ACS

12.4. IMPLEMENTATION AND NUMERICAL EXAMPLE

12.4.1. Major Procedures of the OKA

12.4.2. Simulation of Branch Outage

12.4.3. Numerical Examples

12.5. CONCLUSION

Chapter 13: Optimization of Electrical Distribution Network

13.1. INTRODUCTION

13.2. RADIAL STRUCTURE OF ELECTRICAL DISTRIBUTION NETWORK

13.3. MATHEMATICAL MODEL FOR RECONFIGURATION PROBLEM

13.4. RADIATION DISTRIBUTION NETWORK LOAD FLOW

13.5. DNRC METHODS

13.5.1. Heuristic Method

13.5.2. Spanning Tree Based Algorithm

13.5.3. Matroid Theory Based Algorithm

13.6. ELECTRICAL DISTRIBUTION NETWORK PLANNING

13.6.1 Mathematical Model

13.6.2. Application of Graph Theory

13.6.3. Numerical Example

Chapter 14: Optimal Load Shedding Using Out-of-Kilter Algorithm

14.1. INTRODUCTION

14.2. FORMULATION OF LOAD SHEDDING

14.3. IMPLEMENTATION

14.3.1. Calculation of Weighting Factors by AHP

14.3.2. Network Flow Model

14.4. SIMULATION

14.5. CONCLUSION

Biography.

INDEX.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record and CIP data provided by publisher.

ISBN:

1-61728-566-8

OCLC:

662453172