Power Systems Applications of Graph Theory


Jizhong Zhu (Author) – Chongqing University, P.R. China

Series: Energy Science, Engineering and Technology

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, covers 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


Chapter 1. Introduction

Chapter 2. Basic Concepts of Graph

Chapter 3. Graph Theory

Chapter 4. Network Flow Programming

Chapter 5. Power Flow and Network Flow

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

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

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

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

Chapter 10. Secure and Economic Automatic Generation Control

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

Chapter 12. Automatic Contingency Selection and Ranking

Chapter 13. Optimization of Electrical Distribution Network

Chapter 14. Optimal Load Shedding using Out-of-Kilter Algorithm


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