Graph Database and Graph Computing for Power System Analysis E-Book

Renchang Dai

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: IEEE Press Series on Power Engineering
• Sprache: Englisch

Seitenzahl: 702

Veröffentlichungsjahr: 2023

Beschreibung

Graph Database and Graph Computing for Power System Analysis Understand a new way to model power systems with this comprehensive and practical guide Graph databases have become one of the essential tools for managing large data systems. Their structure improves over traditional table-based relational databases in that it reconciles more closely to the inherent physics of a power system, enabling it to model the components and the network of a power system in an organic way. The authors' pioneering research has demonstrated the effectiveness and the potential of graph data management and graph computing to transform power system analysis. Graph Database and Graph Computing for Power System Analysis presents a comprehensive and accessible introduction to this research and its emerging applications. Programs and applications conventionally modeled for traditional relational databases are reconceived here to incorporate graph computing. The result is a detailed guide which demonstrates the utility and flexibility of this cutting-edge technology. The book's readers will also find: * Design configurations for a graph-based program to solve linear equations, differential equations, optimization problems, and more * Detailed demonstrations of graph-based topology analysis, state estimation, power flow analysis, security-constrained economic dispatch, automatic generation control, small-signal stability, transient stability, and other concepts, analysis, and applications * An authorial team with decades of experience in software design and power systems analysis Graph Database and Graph Computing for Power System Analysis is essential for researchers and academics in power systems analysis and energy-related fields, as well as for advanced graduate students looking to understand this particular set of technologies.

Leseprobe

Table of Contents

Cover

Table of Contents

Series Page

Title Page

Copyright Page

About the Authors

Preface

Acknowledgments

Part I: Theory and Approaches

1 Introduction

1.1 Power System Analysis

1.2 Mathematical Model

1.3 Graph Computing

References

2 Graph Database

2.1 Database Management Systems History

2.2 Graph Database Theory and Method

2.3 Graph Database Operations and Performance

References

3 Graph Parallel Computing

3.1 Graph Parallel Computing Mechanism

3.2 Graph Nodal Parallel Computing

3.3 Graph Hierarchical Parallel Computing

References

4 Large‐Scale Algebraic Equations

4.1 Iterative Methods of Solving Nonlinear Equations

4.2 Direct Methods of Solving Linear Equations

4.3 Indirect Methods of Solving Linear Equations

References

5 High‐Dimensional Differential Equations

5.1 Integration Methods

5.2 Time Step Control

5.3 Initial Operation Condition

5.4 Graph‐Based Transient Parallel Simulation

5.5 Numerical Case Study

5.6 Summary

References

6 Optimization Problems

6.1 Optimization Theory

6.2 Linear Programming

6.3 Nonlinear Programming

6.4 Mixed Integer Optimization Approach

6.5 Optimization Problems Solution by Graph Parallel Computing

References

7 Graph‐Based Machine Learning

7.1 State of Art on PV Generation Forecasting

7.2 Graph Machine Learning Model

7.3 Convolutional Graph Auto‐Encoder [27]

References

Part II: Implementations and Applications

8 Power Systems Modeling

8.1 Power System Graph Modeling

8.2 Physical Graph Model and Computing Graph Model

8.3 Node‐Breaker Model and Graph Representation

8.4 Bus‐Branch Model and Graph Representation

8.5 Graph‐Based Topology Analysis

References

9 State Estimation Graph Computing

9.1 Power System State Estimation

9.2 Graph Computing‐Based State Estimation

9.3 Bad Data Detection and Identification

9.4 Graph‐Based Bad Data Detection Implementation

References

10 Power Flow Graph Computing

10.1 Power Flow Mathematical Model

10.2 Gauss–Seidel Method

10.3 Newton–Raphson Method

10.4 Fast Decoupled Power Flow Calculation

10.5 Ill‐Conditioned Power Flow Problem Solution

References

11 Contingency Analysis Graph Computing

11.1 DC Power Flow

11.2 Bridge Search

11.3 Conjugate Gradient for Postcontingency Power Flow Calculation

11.4 Contingency Analysis Using Convolutional Neural Networks

11.5 Contingency Analysis Graph Computing Implementation

References

12 Economic Dispatch and Unit Commitment

12.1 Classic Economic Dispatch

12.2 Security‐Constrained Economic Dispatch

12.3 Security‐Constrained Unit Commitment

12.4 Numerical Case Study

References

13 Automatic Generation Control

13.1 Classic Automatic Generation Control

13.2 Network Security‐Constrained Automatic Generation Control

13.3 Security‐Constrained AGC Graph Computing

References

14 Small‐Signal Stability

14.1 Small‐Signal Stability of a Dynamic System

14.2 System Linearization

14.3 Small‐Signal Stability Mode

14.4 Single‐Machine Infinite Bus System

14.5 Small‐Signal Oscillation Stabilization

14.6 Eigenvalue Calculation

References

15 Transient Stability

15.1 Transient Stability Theory

15.2 Transient Simulation Model

15.3 Transient Simulation Approach

15.4 Transient Simulation by Graph Parallel Computing

15.5 Numerical Example

References

16 Graph‐Based Deep Reinforcement Learning on Overload Control

16.1 Introduction

16.2 DDPG Algorithm

16.3 Branch Overload Control

16.4 Graph‐Based Deep Reinforcement Learning Implementation

References

17 Conclusions

Appendix

A CIM/E Tables

B Synchronous Machine Model

C Deep Deterministic Policy Gradient Pseudo‐Code

D Security‐Constrained AGC Graph Computing Pseudo‐Code

E Graph‐Based Eigenvalue Calculation Pseudo‐Code

F Graph‐Based Transient Simulation Implementation

Index

IEEE Press Series on Power and Energy Systems

End User License Agreement

List of Tables

Chapter 2

Table 2.1 Data structure modeling in RDBMS and GDBMS.

Table 2.2 Performance test for RDBMS and GDBMS (ms).

Table 2.3 Test environment.

Chapter 3

Table 3.1 Elimination skipped row table.

Table 3.2 Elimination dependence table.

Table 3.3 Node partition for hierarchical parallel.

Chapter 4

Table 4.1 Triple matrix.

Chapter 5

Table 5.1 Accuracy and stability of selected integration methods.

Table 5.2 IEEE 30‐bus modified test system machine data.

Table 5.3 IEEE 30‐bus modified test system exciter data.

Table 5.4 IEEE 30‐bus modified test system governor data.

Chapter 6

Table 6.1 Initial tableau.

Table 6.2 Tableau after the first pivot.

Table 6.3 Tableau

x

4

is selected as leaving variable.

Table 6.4 Tableau after pivot.

Table 6.5 Search iteration by interior‐point method.

Chapter 9

Table 9.1 IEEE 14‐bus test system branch data.

Table 9.2 IEEE 14‐bus test system bus data.

Table 9.3 IEEE 14‐bus test system branch measurements.

Table 9.4 IEEE 14‐bus test system bus measurements.

Chapter 10

Table 10.1 IEEE‐14 bus system bus table.

Table 10.2 IEEE‐14 bus system branch table.

Chapter 11

Table 11.1 Test results for the 1354‐bus system.

Chapter 12

Table 12.1 Unit information table header.

Table 12.2 Unit information.

Table 12.3 IEEE‐14 bus system bus table.

Table 12.4 Thermal unit economic dispatch iteration.

Table 12.5 Hydrothermal system unit economic dispatch iteration.

Table 12.6 Unit information table header.

Table 12.7 IEEE‐14 bus system branch table.

Table 12.8 Generation shift factor matrix.

Table 12.9 SCED iteration.

Chapter 13

Table 13.1 Modified IEEE‐14 bus system bus table.

Table 13.2 IEEE‐14 bus system bus table.

Table 13.3 IEEE‐14 bus system bus table.

Table 13.4 Security‐constrained automatic generation control iteration.

Table 13.5 Security‐constrained automatic generation control iteration.

Chapter 14

Table 14.1 System parameters.

Table 14.2 System parameters.

Table 14.3 Small‐signal stability analysis result.

Table 14.4 Small‐signal stability analysis result.

Table 14.5 State matrix table header.

Chapter 15

Table 15.1 Self‐excited AVR parameters.

Table 15.2 Separately excited AVR parameters.

Table 15.3 Governor parameters.

Table 15.4 PSS parameters.

Table 15.5 Generator model parameter table header.

Table 15.6 Self-excited AVR model parameter table header.

Table 15.7 Separately excited AVR parameter table header.

Table 15.8 Generic governor model parameter table header.

Table 15.9 PSS model parameter table header.

Table 15.10 IEEE 14‐bus test system branch data.

Table 15.11 IEEE 14‐bus test system bus data.

Table 15.12 IEEE 14‐bus modified test system machine data.

Table 15.13 IEEE 14‐bus modified test system exciter data.

Table 15.14 IEEE 14‐bus modified test system governor data.

Table 15.15 IEEE 14‐bus modified test system power flow solution.

Table 15.16 Unit steady‐state equilibrium points.

Table 15.17 IEEE 14‐bus modified test system generator injection current.

Table 15.18 Bus voltage updates.

Table 15.19 Generator bus and faulted bus voltage.

Appendix

Table A.1 Base value table in CIM/E model.

Table A.2 Substation table in CIM/E model.

Table A.3 Bus table in CIM/E model.

Table A.4 ACline table in CIM/E model.

Table A.5 Unit table in CIM/E model.

Table A.6 Transformer table in CIM/E model.

Table A.7 Load table in CIM/E model.

Table A.8 Shunt compensator table in CIM/E model.

Table A.9 Series compensator table in CIM/E model.

Table A.10 Converter table in CIM/E model.

Table A.11 DC line table in CIM/E model.

Table A.12 Island table in CIM/E model.

Table A.13 Topological node table in CIM/E model.

Table A.14 Breaker table in CIM/E model.

Table A.15 Disconnector table in CIM/E model.

Table A.16 Vertex attributes in bus‐branch model.

Table A.17 Edge attributes in bus‐branch model.

Table A.18 Generator parameters.

Table A.19 Flowgate information table header.

List of Illustrations

Chapter 2

Figure 2.1 One‐line diagram of 5‐bus system.

Figure 2.2 5‐Bus system graph model.

Figure 2.3 MapReduce parallel computing mechanism.

Figure 2.4 The graph analytic platform.

Figure 2.5 Graph computing platform.

Figure 2.6 6‐bus distribution system.

Figure 2.7 6‐bus distribution system graph model.

Figure 2.8 MapReduce and backward‐forward sweep.

Figure 2.9 Non‐weighted graph partitioning.

Figure 2.10 Weighted graph partitioning.

Chapter 3

Figure 3.1 A generic BSP model.

Figure 3.2 Graph parallelism model.

Figure 3.3 BSP parallel scheme.

Figure 3.4 Admittance matrix formation by graph. (a) admittance matrix; (b) ...

Figure 3.5 MapReduce by graph.

Figure 3.6 Graph structure

G

(

A

) for matrix

A

.

Figure 3.7 Column 1 elimination. (a) eliminate column 1; (b) fill‐ins after ...

Figure 3.8 Column 2 elimination. (a) eliminate column 2; (b) fill‐ins after ...

Figure 3.9 Column 3 elimination. (a) eliminate column 3; (b) fill‐ins after ...

Figure 3.10 Filled graph structure

G

+

(

A

).

Figure 3.11 Elimination tree

T

(

A

).

Chapter 4

Figure 4.1 Example of the basic principle of PageRank.

Figure 4.2 Failure of Newton–Raphson method. (a) runaway; (b) flat spot; (c)...

Figure 4.3 4‐bus system.

Figure 4.4 Sparse matrix compressed sparse row.

Figure 4.5 Sparse matrix CSC.

Figure 4.6 Undirected graph.

Figure 4.7 Relation between symmetric matrix and undirected graph.

Figure 4.8 4‐bus system with phase shifting transformer.

Figure 4.9 Directed graph.

Figure 4.10 Directed graph representing matrix

L

.

Chapter 5

Figure 5.1 Trapezoidal rule.

Figure 5.2 Absolute stability regions. (a) forward Euler; (b) backward Euler...

Figure 5.3 TS‐EMT interaction protocols.

Figure 5.4 TS‐EMT interface.

Figure 5.5 EMT equivalent sequence current injection to TS.

Figure 5.6 Generator equivalent circuit.

Figure 5.7 Generator state vector.

Figure 5.8 DAE construction of power system.

Figure 5.9 Power system transient simulation flow chart.

Figure 5.10 Simulation results by fixed time step.

Figure 5.11 Simulation results by variable time step.

Figure 5.12 Simulation result details by fixed time step.

Figure 5.13 Simulation result details by variable time step.

Figure 5.14 Simulation time steps by the two approaches.

Figure 5.15 Differential equation truncation errors by the two approaches.

Figure 5.16 Differential equation detailed truncation errors.

Chapter 6

Figure 6.1 Search process on polytope by simplex method.

Figure 6.2 Simplex method solving process.

Figure 6.3 Search path on polytope by interior‐point method.

Figure 6.4 Dogleg step.

Figure 6.5 The illustration of branch and bound method.

Figure 6.6 Directed graph.

Chapter 7

Figure 7.1 Photovoltaic power station correlation heat map.

Figure 7.2 Graph model of the 75 nodes and 464 edges.

Figure 7.3 General structure of the auto‐encoder.

Figure 7.4 Structure of graph auto‐encoder neural network.

Figure 7.5 Learning structure of convolutional auto-encoder.

Figure 7.6 Testing structure of convolutional auto‐encoder.

Figure 7.7 Convolutional graph auto‐encoder.

Figure 7.8 Trained generative model.

Chapter 8

Figure 8.1 Conceptual bus‐branch graph model.

Figure 8.2 Conceptual node‐break graph model.

Figure 8.3 CIM/XML model.

Figure 8.4 CIM/E model.

Figure 8.5 Substation representation in one line diagram and CIM/E. (a) one ...

Chapter 9

Figure 9.1 A generalized structure of node‐

i

‐centered system graph.

Figure 9.2 Diagonal entry (taking node

i

as an example).

Figure 9.3 1‐step entry (taking node

a

1

as an example).

Figure 9.4 2‐step entry (taking node

a

2

as an example).

Figure 9.5 IEEE 14‐bus system.

Figure 9.6 Graph model of IEEE 5‐bus system.

Chapter 10

Figure 10.1 A zero injection load bus with degree 1.

Figure 10.2 A zero injection load bus with degree 2.

Figure 10.3 The reconfigured network for zero injection load bus with degree...

Figure 10.4 A zero injection load bus with degree 3.

Figure 10.5 The reconfigured network for zero injection load bus with degree...

Chapter 11

Figure 11.1 Example of a connected undirected graph.

Figure 11.2 Tarjan's algorithm illustration (a).

Figure 11.3 Tarjan's algorithm illustration (b).

Figure 11.4 Tarjan's algorithm illustration (c).

Figure 11.5 Tarjan's algorithm illustration (d).

Figure 11.6 Tarjan's algorithm illustration (f).

Figure 11.7 Postcontingency matrix changes.

Figure 11.8 Feedforward neural network general structure.

Figure 11.9 Convolutional neural network general structure.

Figure 11.10 1354‐bus system adjacency lower triangular matrix.

Figure 11.11 1354‐bus system adjacency lower triangular matrix (after RCM re‐ord...

Chapter 12

Figure 12.1 Graph computing based power market simulation framework [20].

Chapter 13

Figure 13.1 Turbine‐governor diagram.

Figure 13.2 IEEE type 3 speed‐governor model IEEEG3 transfer function.

Figure 13.3 Speed and power transfer function.

Figure 13.4 Generating unit control block diagram.

Figure 13.5 Generating unit control block diagram with droop function.

Figure 13.6 Frequency droop function.

Figure 13.7 Governor droop function and load frequency dependence.

Figure 13.8 Single line diagram of the IEEE 14‐bus system.

Figure 13.9 The IEEE 14‐bus system zonal model.

Figure 13.10 Primary frequency response with 5% load reduction.

Figure 13.11 Primary frequency response with 5% load increase.

Figure 13.12 Generating unit control block diagram with supplementary contro...

Figure 13.13 Governor supplementary control.

Figure 13.14 Two‐area interconnected system.

Figure 13.15 Electrical equivalent system.

Figure 13.16 Two‐area interconnected system frequency control.

Figure 13.17 Two-area interconnected system AGC control.

Figure 13.18 Graph-based security-constrained AGC flowchart.

Chapter 14

Figure 14.1 Single‐machine infinite bus system equivalent circuit.

Figure 14.2 Single‐machine infinite bus system with classical generator mode...

Figure 14.3 Generator equivalent circuits in

d–q

reference frame. (a)

Figure 14.4 Synchronous machine third‐order model vector diagram.

Figure 14.5 Single‐machine infinite bus system with third‐order generator mo...

Figure 14.6 Excitation system transfer function.

Figure 14.7 Excitation system transfer function with power system stabilizer...

Figure 14.8 Power system stabilizer transfer function.

Chapter 15

Figure 15.1 Fault‐on trajectory.

Figure 15.2 System block diagram.

Figure 15.3 Self‐excited AVR transfer function block diagram.

Figure 15.4 Separately excited AVR transfer function block diagram.

Figure 15.5 Generic speed‐governor transfer function.

Figure 15.6 Type I PSS function block diagram.

Figure 15.7 Flowchart of sequential method to transient simulation.

Figure 15.8 Synchronous machine steady‐state phasor diagram.

Figure 15.9 Single‐line diagram of the IEEE 14‐bus system.

Figure 15.10 Bus voltage.

Figure 15.11 Generator rotor speed.

Figure 15.12 Generator field voltage.

Figure 15.13 Generator

d

‐axis transient voltage.

Figure 15.14 Generator

q

‐axis transient voltage.

Figure 15.15 Generator

d

‐axis subtransient voltage.

Figure 15.16 Generator

q

‐axis subtransient voltage.

Chapter 16

Figure 16.1 Actor‐critic algorithm structure.

Appendix

Figure A.1 Synchronous machine phasor direction convention diagram.

Figure A.2 Synchronous machine steady‐state phasor diagram.

Figure A.3 Self‐excited AVR transfer function block diagram.

Figure A.4 Generic speed‐governor transfer function.

Figure A.5 Type I power system stabilizer function block diagram.

Guide

Cover Page

Series Page

Title Page

Copyright Page

About the Authors

Preface

Acknowledgments

Table of Contents

Begin Reading

Appendix

Index

IEEE Press Series on Power and Energy Systems

WILEY END USER LICENSE AGREEMENT

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IEEE Press445 Hoes LanePiscataway, NJ 08854

IEEE Press Editorial BoardSarah Spurgeon, Editor in Chief

Jón Atli Benediktsson  

Behzad Razavi  

Jeffrey Reed  

Anjan Bose  

Jim Lyke  

Diomidis Spinellis  

James Duncan  

Hai Li  

Adam Drobot  

Amin Moeness  

Brian Johnson  

Tom Robertazzi  

Desineni Subbaram Naidu  

Ahmet Murat Tekalp  

Graph Database and Graph Computing for Power System Analysis

Renchang Dai

Puget Sound EnergyBellevue, WA, USA

Guangyi Liu

Envision DigitalSan Jose, CA, USA

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Library of Congress Cataloging‐in‐Publication Data:

Names: Dai, Renchang, author. | Liu, Guangyi (Scientist), author.Title: Graph database and graph computing for power system analysis / Renchang Dai, Guangyi Liu.Description: Hoboken, New Jersey : Wiley-IEEE Press, [2024] | Includes index.Identifiers: LCCN 2023023393 (print) | LCCN 2023023394 (ebook) | ISBN 9781119903864 (cloth) | ISBN 9781119903871 (adobe pdf) | ISBN 9781119903888 (epub)Subjects: LCSH: Graph databases. | Electric power systems.Classification: LCC QA76.9.D32 D33 2024 (print) | LCC QA76.9.D32 (ebook) | DDC 005.75/8--dc23/eng/20230602LC record available at https://lccn.loc.gov/2023023393LC ebook record available at https://lccn.loc.gov/2023023394

Cover Design: WileyCover Image: © Alejandro Mendoza R/Shutterstock

About the Authors

Renchang Dai, PhD, is a consulting engineer and project manager at Puget Sound Energy. He received his PhD degree in electrical engineering from Tsinghua University, China, in 2001.

Dr. Dai has worked on a variety of power system problems, including power system planning, operations, and control. He was the principal engineer and group manager for Global Energy Interconnection Research Institute North America, where he led a team of engineers in researching and developing graph database and graph computing technologies for power system planning and operations.

Dr. Dai was a team leader for GE Energy. In GE Energy, he designed, developed, and implemented Energy Management System. He was also a founding member of the GE Energy Consulting Smart Grid Center of Excellence, where he consulted on smart grid deployment and renewable energy grid integration projects. In 2005, when he was a lead scientist in GE Global Research, he was awarded the GE Global Technical Award for his contributions to the development of wind turbine generator fault ride through technology.

Dr. Dai is a senior member of the IEEE. He has worked intensively on graph‐based power system analysis and has published over 100 papers in international journals and conferences.

Guangyi Liu, PhD, is a chief scientist at Envision Digital. He is leading a team of engineers to develop power system application software that is based on graph database and graph computing technologies. He received his PhD degree in electrical engineering from the China Electric Power Research Institute, China, in 1990.

Dr. Liu has worked on a variety of power system research fields, including Energy Management System (EMS), Distribution Management System (DMS), Electricity Market, Active Distribution Network, and Big Data. He was the principal engineer and chief technology officer for Global Energy Interconnection Research Institute North America, where he led a team of engineers in researching and developing graph database and graph computing technologies for power system calculation, analysis, and optimization.

Dr. Liu is a senior member of the IEEE and a fellow of the Chinese Society of Electrical Engineering. He has worked intensively on power system analysis and optimization, and he has published over 200 papers in international journals and conferences.

Preface

We started to work on power system analysis decades ago. Improving power system analysis computation efficiency is an ongoing task and a challenge for online applications and offline analyses in the power industry. The tireless and remarkable efforts have been endeavored by researchers and engineers trying to achieve real‐time steady‐state, dynamic, and optimization applications. Keeping this ambition in mind, the idea of graph computing was inspired at an occasional conservation with Professor Shoucheng Zhang from Stanford University in 2015 when he introduced a start‐up company and their work on graph databases to us. The perfect match of graph nature and power network structure sparked the long exploration and journey of researching and developing graph computing theory, algorithms, methods, approaches, and applications for years. This book is a comprehensive summary and knowledge sharing of our research and engineering work on graph computing for power system analysis.

This book is divided into two parts. Part I devotes the first seven chapters to highlighting the theoretical methods and approaches. Part II is composed of Chapters 8–17 on practical implementations and applications. Part I serves prerequisites of graph computing with basics and advances of graph databases, graph parallel computing, and knowledge of solving algebraic equations, optimization problems, differential equations, and their combinations. Part II provides a comprehensive illustration of graph‐based power system modeling, analysis approaches, and implementations with detailed graph query scripts. The implemented applications presented in Part II cover power system topology analysis, state estimation, power flow calculation, contingency analysis, security‐constrained economic dispatch, security‐constrained unit commitment, automatic generation control, small‐signal stability, transient stability, and deep reinforcement learning.

Currently, the practice of power system modeling focuses on using relational databases. In relational databases, data are organized and managed in tables. The relationships between tables are connected by separated tables or by using a join operation to search common attributes in different tables to find the relationships. In this mechanism, it is challenging to maintain and manipulate a large dataset in a relational database.

Contrary to the relational database, a graph database uses graph structures for semantic queries with nodes and edges to store data. The essential differences between graph databases and relational databases are that the edge directly defines the data relationship and graph databases are designed for parallel computing. Graph computing models power systems as a graph which is consistent with the fact that power system physically is a graph – buses are connected by branches as a graph. The graph data structure tells the topology of the power network and the relations of power system components naturally. The graph computing mechanism by using queries on nodes and graph partitions, promotes parallel computing for power system applications.

Graph databases are new to the power industry. Graph computing is novel to researchers and engineers. The main objective of this book is to provide a roadmap and guidance to readers to learn the alternative and innovative approaches to modeling and solving power system problems from scratch. For this purpose, the processes of defining vertex, edge, and graph schema, creating a loading job, and developing detailed graph queries are demonstrated. The scripts for each power system analysis are provided and explained in detail to facilitate readers to gradually and comprehensively master graph computing. To make this book a reference to graduate students, illustrative problems are presented and hands‐on experiences in graph computing design and programming are provided by detailed scripts.

The graph computing research activities are still progressing. We believe that graph computing has great potential in various power system analyses. We hope this book can invite and inspire researchers and engineers to study and research graph databases and graph computing and apply the graph computing theory and approaches to develop power system applications.

Renchang Dai

Guangyi Liu

Acknowledgments

This book is a result of the fascinating journey of our study and research work for decades. We firstly acknowledge our research advisors, Professor Ming Ding from the Hefei University of Technology, Professor Boming Zhang from Tsinghua University, and Professor Erkeng Yu from the China Electric Power Research Institute, for ushering us into the world of power system analysis and leading us into the research area of power system real‐time applications. The knowledge and experience they shared with us along with their advice, influence our research to this day.

We also acknowledge our research team for their contributions and support on this challenging and rewarding work for many years. A great thanks goes to Dr. Ting Chen, Mr. Hong Fan, Dr. Chen Yuan, Dr. Jingjin Wu, Dr. Yiting Zhao, Dr. Jun Tan, Dr. Jiangpeng Dai, Dr. Yongli Zhu, Dr. Longfei Wei, Dr. Xiang Zhang, Dr. Peng Wei, Dr. Yachen Tang, Mr. Kewen Liu, Mr. Wendong Zhu, Mrs. Tingting Liu, Mrs. Bowen Kan, Mr. Haiyun Han, Mr. Letian Teng, Dr. Kai Xie, Mr. Zhiwei Wang, Dr. Xi Chen, Mrs. Ziyan Yao, Dr. Wei Feng, Dr. Yijing Liu, Mrs. Jing Hong, Mr. Huaming Zhang, Dr. Saeed D. Manshadi, Dr. Mariana Kamel, Dr. Yawei Wang, Mr. Yanan Lyu, and many other colleagues and interns, for their contributions on the research and development of the material presented in this book and wonderful ideas about the graph computing related research topics.

We are grateful and thankful to Professor Fran Li from the University of Tennessee, Knoxville, Professor Jianhui Wang from Southern Methodist University, Professor Hsiao‐Dong Chiang from Cornell University, and Professor Yinyu Ye from Stanford University for partnering with us on the research and development work and fantastic discussion on graph computing.

Last but not least, we would like to thank our families. We understand writing this manuscript is not an easy task from day one. The real journey is even harder than expected, with unexpected detours. We express our heartfelt thanks to them for their support and understanding over the past several years.

Renchang Dai

Guangyi Liu

Part ITheory and Approaches