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Power Systems Applications of Graph Theory
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Authors: Jizhong Zhu (Chongqing University, P.R. China) 
Book Description:
There are several books on the applications of graph theory, but none of them are related to power systems applications. This book attempts to cover all applications of graph theory in the area of power systems. It consists of two parts. The first part, containing four Chapters, briefly introduces the basic concepts of graph theory, major properties, theorems, and algorithms in graph theory and network flow programming. This definitive treatment makes graph theory easy to understand. The second part, containing 10 Chapters, is the practical applications of graph theory and network flow programming to all kinds of power systems problems, which is the key part of the book. These applications include network flow calculation of power flow, classical economic power dispatch, security constrained economic dispatch, multi-areas system economic dispatch, reactive power optimization and pricing in multi-area environment, hydro-thermal power system operation, power system state estimation, secure economic automatic generation control, automatic contingency selection, distribution network optimization, and optimal load shedding. The treatment of each application includes the mathematical representation of power system problem, its relationship with graph theory and network flow programming, as well as the implementations accompanied by examples of power system application problem, solution, and results analysis. Each Chapter contains the related references that collectively form an extensive guide to the primary research literature.

Table of Contents:
Preface pp. i-ix

1. Introduction pp.1-4

2. Basic Concepts of Graph pp.5-20
2.1 Introduction
2.2 Basic Concepts
2.3 Basic Structural Properties

3. Graph Theory pp.21-58
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

4. Network Flow Programming pp.59-96
4.1 Network
4.2 Maximum Flow Problem
4.1.1 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
4.4.2.1 Delaunay Triangulation
4.4.2.2 EMST Algorithm
4.4 The Transportation Problem

5. Power Flow and Network Flow pp.97-118
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

6. Minimum Cost Flow Method For Power Systems Economic Dispatch pp.119-142
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
6.4.2.1 Neglect Network Losses
6.4.2.2 Consider Network Losses
6.4.3 Numerical Example

7. Application of Out-of-Kilter Algorithm To Economic Power Dispatch pp.143-176
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

8. Application of Graph Theory to Power Systems State Estimation
8.1 Introduction pp.177-194
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

9. Application of Nonlinear Convex Network Flow Programming to Multi-Area System Economic Dispatch pp.195-216
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

10. Secure and Economic Automatic Generation Control pp.217-234
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

11. VAR Optimization and Pricing in Multi-Area Power System pp.235-250
11.1 Introduction
11.2 Optimal Model in Multi-Areas
11.3 VAR Pricing In Multi-Areas
11.4 Selection of VAR Sources
11.5 Test Results and Analysis
11.6 Conclusion

12. Automatic Contingency Selection and Ranking pp.251-266
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

13. Optimization of Electrical Distribution Network pp.267-296
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
13.5.4. Numerical Examples
13.6 Electrical Distribution Network Planning
13.6.1 Mathematical Model
13.6.2 Application of Graph Theory
13.6.3 Numerical Example

14. Optimal Load Shedding using Out-of-Kilter Algorithm pp.297-314
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

Index pp.315-320

   Series:
      Energy Science, Engineering and Technology
   Binding: Hardcover
   Pub. Date: 2011
   Pages: 329
   ISBN: 978-1-60741-364-6
   Status: AV
  
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
  
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Power Systems Applications of Graph Theory