Power System Simulation Using Semi-Analytical Methods

Robust coverage of semi-analytical and traditional numerical methods for power system simulation

In Power System Simulation Using Semi-Analytical Methods, distinguished researcher Dr. Kai Sun delivers a comprehensive treatment of semi-analytical simulation and current semi-analytical methods for power systems. The book presents semi-analytical solutions on power system dynamics via mathematical tools, and covers parallel contingency analysis and simulations. The author offers an overview of power system simulation and contingency analysis supported by data, tables, illustrations, and case studies on realistic power systems and experiments.

Readers will find open-source code in MATLAB along with examples for key algorithms introduced in the book. You’ll also find:

• A thorough background on power system simulation, including models, numerical solution methods, and semi-analytical solution methods
• Comprehensive explorations of semi-analytical power system simulation via a variety of mathematical methods such as the Adomian decomposition, differential transformation, homotopy analysis and holomorphic embedding methods.
• Practical discussions of semi-analytical simulations for realistic large-scale power grids
• Fulsome treatments of parallel power system simulation

Perfect for power engineers and applied mathematicians with an interest in high-performance simulation of power systems and other large-scale network systems, Power System Simulation Using Semi-Analytical Methods will also benefit researchers and postgraduate students studying power system engineering.

Kai Sun, PhD, is a Professor with the Department of Electrical Engineering and Computer Science at the University of Tennessee in Knoxville. He is the author of Power System Control under Cascading Failures: Understanding, Mitigation and System Restoration and has co-authored more than ten IEEE journal papers on semi-analytical methods for power system simulation.

PREFACE

by Kai Sun

1 POWER SYSTEM SIMULATION: FROM NUMERICAL TO SEMI-ANALYTICAL

by Kai Sun

1.1 Timescales of Simulation       4

1.2 Power System Models            7

1.2.1 Overview 7

1.2.2 Generator Models 10

1.2.3 Controller Models 13

1.2.4 Load Models           18

1.2.5 Network Model     21

1.2.6 Classical Power System Model        22

1.3 Numerical Simulation              25

1.3.1 Explicit Integration Methods            26

1.3.2 Implicit Integration Methods           29

1.3.3 Solving Differential-Algebraic Equations      33

1.4 Semi-Analytical Simulation    35

1.4.1 Drawbacks with Numerical Simulations       35

1.4.2 Emerging Methods for Semi-Analytical Power System Simulation    36

1.4.3 Approaches to Semi-Analytical Solutions    38

1.4.4 Forms of Semi-Analytical Solutions 46

1.4.5 Schemes on Semi-Analytical Power System Simulation         48

1.5 Parallel Power System Simulation      50

1.5.1 Parallelization in Space       51

1.5.2 Parallelization in Time         52

1.5.3 Parallelization of Semi-Analytical Solutions 55

1.6 Final Remark              56

References         57

2 POWER SYSTEM SIMULATION USING POWER SERIES-BASED SEMI-ANALYTICAL METHOD

by Bin Wang

2.1. Power Series-Based SAS for Simulating Power System ODEs

2.1.1. Power Series-Based SAS for ODEs

2.1.2. SAS-Based Fault-on Trajectory Simulation and Its Application in Direct Methods

2.2. Power Series-Based SAS for Simulating Power System DAEs

2.2.1. Power Series-Based SAS for Power System DAEs

2.2.2. SAS-Based Simulation of Power System DAEs

2.3. Adaptive Time-Stepping Method for SAS-Based

2.3.1. Error-Rate Upper Bound

2.3.2. Adaptive Time-Stepping for SAS-Based Simulation

2.4. Numerical Examples

2.4.1. SAS vs. RK4 and BDF

2.4.2. SAS Derivation

2.4.3. Application of SAS-Based Simulation on Polish 2383-Bus Power System

3 POWER SYSTEM SIMULATION USING DIFFERENTIAL TRANSFORMATION METHOD by Yang Liu

3.1 Introduction to Differential Transformation  1

3.2 Solving the Ordinary Differential Equation Model       6

3.2.1 Derivation Process               6

3.2.2 Solution Algorithm               11

3.2.3 Case Study               13

3.3 Solving the Differential-Algebraic Equation Model      22

3.3.1 Basic Idea 22

3.3.2 Derivation Process               24

3.3.3 Solution Algorithm               27

3.3.4 Case Study               28

3.4 Broader Applications               32

3.5 Conclusions and Future Directions     33

References         34

4 ACCELERATED POWER SYSTEM SIMULATION USING ANALYTIC CONTINUATION TECHNIQUES

by Chengxi Liu

4.1 Introduction to Analytic Continuation              3

4.1.1 Direct Method (or matrix method) 5

4.1.2 Continued fractions (i.e. Viskovatov method)           7

4.2 Finding Semi-Analytical Solutions Using Padé Approximants  8

4.2.1 Semi-Analytical Solution Using Padé Approximants 8

4.2.2 Padé Approximants of Power System Differential Equations              11

4.2.3 Examples  13

4.3 Fast Power System Simulation Using Continued Fractions       19

4.3.1 The Proposed Two-Stage Simulation Scheme           20

4.3.2 Continued Fractions-Based Semi-Analytical Solutions            22

4.3.3 Adaptive Time Interval Based on Priori Error Bound of Continued Fractions 25

4.3.4 Examples  28

4.4 Conclusions 33

References         33

5 POWER SYSTEM SIMULATION USING MULTI-STAGE ADOMIAN DECOMPOSITION METHODS

by Nan Duan

5.1 Introduction to Adomian Decomposition Method      2

5.1.1 Solving Deterministic Differential Equations              2

5.1.2 Solving Stochastic Differential Equations     3

5.2 Adomian Decomposition of Deterministic Power System Models        3

5.2.1 Applying Adomian Decomposition Method to Power Systems           3

5.2.2 Convergence and Time Window of Accuracy             6

5.2.3 Adaptive Time Window      11

5.2.4 Simulation Scheme              11

5.2.5 Examples  14

5.3 Adomian Decomposition of Stochastic Power System Models               27

5.3.1 Single Machine Infinite Bus System with a Stochastic Load  27

5.3.2 Examples  30

5.4 Large-scale Power System Simulations Using Adomian Decomposition Method            33

References         34

6 APPLICATION OF HOMOTOPY METHODS IN POWER SYSTEMS SIMULATIONS

by Gurunath Gurrala and Francis C Joseph

6.1. Introduction

6.2. The Homotopy Method

6.3. Application of Homotopy methods to Power Systems

6.3.1. Generator Model for Transient Stability

6.4. Multimachine Simulations

6.4.1. Impact of Number of Terms Considered

6.4.2. Effect of c

6.5. Application of Homotopy for Error Estimation

6.5.1. Adaptive Step Size Adjustment based Modified Euler

6.5.2. Non-Iterative Adaptive Step Size Adjustment

6.5.3. Simulation Results

6.5.4. Tracking of LTE

6.5.5. Accuracy with Variation of Desired LTE

6.5.6. Computational Time and Speedup

6.6. Summary   

7 UTILIZING SEMI-ANALYTICAL METHODS IN PARALLEL-IN-TIME POWER SYSTEM SIMULATIONS

by Byungkwon Park

7.1. Introduction to the Parallel-in-Time (Parareal Algorithm) Simulation

7.1.1. Overview of Parareal Algorithm

7.1.2. The derivation of Parareal algorithm

7.1.3. Implementation of Parareal Algorithm

7.2. Examination of Semi-Analytical Solution Methods in the Parareal Algorithm

7.2.1. Adomian Decomposition Method

7.2.2. Homotopy Analysis Method

7.2.3. Summary

7.3. Numerical Case Study

7.3.1. Validation of Parareal Algorithm

7.3.2. Benefits of Semi-Analytical Solution methods

7.3.3. Results with the High Performance Computing Platform

7.3.4. Results with Variable Order Variable Step Adaptive Parareal algorithm

7.4. Conclusions

8 POWER SYSTEM SIMULATION USING HOLOMORPHIC EMBEDDING METHODS

by Rui Yao, Kai Sun, and Feng Qiu

8.1. Holomorphic Embedding from Steady State to Dynamics

8.1.1. Holomorphic embedding formulations

8.1.2. VSA using holomorphic embedding

8.1.3. Test cases

8.1.4. Summary of the Section

8.2. Generic Holomorphic Embedding for Dynamic Security Analysis

8.2.1. General holomorphic embedding

8.2.2. Solve state after instant switches

8.2.3. Overall Dynamic simulation process

8.2.4. Test cases

8.2.5. Summary of Section

8.3. Extended-term Hybrid Simulation

8.3.1. Steady-state & Dynamic Hybrid Simulation

8.3.2. Extended-term Simulation Framework

8.3.3. Experiments

8.3.4. Summary of Section

8.4. Robust Parallel or Distributed Simulation

8.4.1. Steady-state contingency analysis: problem formulation and state of the art

8.4.2. Partitioned holomorphic embedding (PHE)

8.4.3. Parallel and Distributed Computation

8.4.4. Experiment on large-scale system

8.4.5. Summary of Section

Index

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