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 Paď Approximants 8
4.2.1 Semi-Analytical Solution Using Paď Approximants 8
4.2.2 Paď 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.