Power System Simulation Using Semi-Analytical Methods

ISBN-13: 9781119988014 / Angielski / Twarda / 2023

Sun

Spis treści

PREFACEby Kai Sun1 POWER SYSTEM SIMULATION: FROM NUMERICAL TO SEMI-ANALYTICALby Kai Sun1.1 Timescales of Simulation 41.2 Power System Models 71.2.1 Overview 71.2.2 Generator Models 101.2.3 Controller Models 131.2.4 Load Models 181.2.5 Network Model 211.2.6 Classical Power System Model 221.3 Numerical Simulation 251.3.1 Explicit Integration Methods 261.3.2 Implicit Integration Methods 291.3.3 Solving Differential-Algebraic Equations 331.4 Semi-Analytical Simulation 351.4.1 Drawbacks with Numerical Simulations 351.4.2 Emerging Methods for Semi-Analytical Power System Simulation 361.4.3 Approaches to Semi-Analytical Solutions 381.4.4 Forms of Semi-Analytical Solutions 461.4.5 Schemes on Semi-Analytical Power System Simulation 481.5 Parallel Power System Simulation 501.5.1 Parallelization in Space 511.5.2 Parallelization in Time 521.5.3 Parallelization of Semi-Analytical Solutions 551.6 Final Remark 56References 572 POWER SYSTEM SIMULATION USING POWER SERIES-BASED SEMI-ANALYTICAL METHODby Bin Wang2.1. Power Series-Based SAS for Simulating Power System ODEs2.1.1. Power Series-Based SAS for ODEs2.1.2. SAS-Based Fault-on Trajectory Simulation and Its Application in Direct Methods2.2. Power Series-Based SAS for Simulating Power System DAEs2.2.1. Power Series-Based SAS for Power System DAEs2.2.2. SAS-Based Simulation of Power System DAEs2.3. Adaptive Time-Stepping Method for SAS-Based2.3.1. Error-Rate Upper Bound2.3.2. Adaptive Time-Stepping for SAS-Based Simulation2.4. Numerical Examples2.4.1. SAS vs. RK4 and BDF2.4.2. SAS Derivation2.4.3. Application of SAS-Based Simulation on Polish 2383-Bus Power System3 POWER SYSTEM SIMULATION USING DIFFERENTIAL TRANSFORMATION METHOD by Yang Liu3.1 Introduction to Differential Transformation 13.2 Solving the Ordinary Differential Equation Model 63.2.1 Derivation Process 63.2.2 Solution Algorithm 113.2.3 Case Study 133.3 Solving the Differential-Algebraic Equation Model 223.3.1 Basic Idea 223.3.2 Derivation Process 243.3.3 Solution Algorithm 273.3.4 Case Study 283.4 Broader Applications 323.5 Conclusions and Future Directions 33References 344 ACCELERATED POWER SYSTEM SIMULATION USING ANALYTIC CONTINUATION TECHNIQUESby Chengxi Liu4.1 Introduction to Analytic Continuation 34.1.1 Direct Method (or matrix method) 54.1.2 Continued fractions (i.e. Viskovatov method) 74.2 Finding Semi-Analytical Solutions Using Padé Approximants 84.2.1 Semi-Analytical Solution Using Padé Approximants 84.2.2 Padé Approximants of Power System Differential Equations 114.2.3 Examples 134.3 Fast Power System Simulation Using Continued Fractions 194.3.1 The Proposed Two-Stage Simulation Scheme 204.3.2 Continued Fractions-Based Semi-Analytical Solutions 224.3.3 Adaptive Time Interval Based on Priori Error Bound of Continued Fractions 254.3.4 Examples 284.4 Conclusions 33References 335 POWER SYSTEM SIMULATION USING MULTI-STAGE ADOMIAN DECOMPOSITION METHODSby Nan Duan5.1 Introduction to Adomian Decomposition Method 25.1.1 Solving Deterministic Differential Equations 25.1.2 Solving Stochastic Differential Equations 35.2 Adomian Decomposition of Deterministic Power System Models 35.2.1 Applying Adomian Decomposition Method to Power Systems 35.2.2 Convergence and Time Window of Accuracy 65.2.3 Adaptive Time Window 115.2.4 Simulation Scheme 115.2.5 Examples 145.3 Adomian Decomposition of Stochastic Power System Models 275.3.1 Single Machine Infinite Bus System with a Stochastic Load 275.3.2 Examples 305.4 Large-scale Power System Simulations Using Adomian Decomposition Method 33References 346 APPLICATION OF HOMOTOPY METHODS IN POWER SYSTEMS SIMULATIONSby Gurunath Gurrala and Francis C Joseph6.1. Introduction6.2. The Homotopy Method6.3. Application of Homotopy methods to Power Systems6.3.1. Generator Model for Transient Stability6.4. Multimachine Simulations6.4.1. Impact of Number of Terms Considered6.4.2. Effect of c6.5. Application of Homotopy for Error Estimation6.5.1. Adaptive Step Size Adjustment based Modified Euler6.5.2. Non-Iterative Adaptive Step Size Adjustment6.5.3. Simulation Results6.5.4. Tracking of LTE6.5.5. Accuracy with Variation of Desired LTE6.5.6. Computational Time and Speedup6.6. Summary7 UTILIZING SEMI-ANALYTICAL METHODS IN PARALLEL-IN-TIME POWER SYSTEM SIMULATIONSby Byungkwon Park7.1. Introduction to the Parallel-in-Time (Parareal Algorithm) Simulation7.1.1. Overview of Parareal Algorithm7.1.2. The derivation of Parareal algorithm7.1.3. Implementation of Parareal Algorithm7.2. Examination of Semi-Analytical Solution Methods in the Parareal Algorithm7.2.1. Adomian Decomposition Method7.2.2. Homotopy Analysis Method7.2.3. Summary7.3. Numerical Case Study7.3.1. Validation of Parareal Algorithm7.3.2. Benefits of Semi-Analytical Solution methods7.3.3. Results with the High Performance Computing Platform7.3.4. Results with Variable Order Variable Step Adaptive Parareal algorithm7.4. Conclusions8 POWER SYSTEM SIMULATION USING HOLOMORPHIC EMBEDDING METHODSby Rui Yao, Kai Sun, and Feng Qiu8.1. Holomorphic Embedding from Steady State to Dynamics8.1.1. Holomorphic embedding formulations8.1.2. VSA using holomorphic embedding8.1.3. Test cases8.1.4. Summary of the Section8.2. Generic Holomorphic Embedding for Dynamic Security Analysis8.2.1. General holomorphic embedding8.2.2. Solve state after instant switches8.2.3. Overall Dynamic simulation process8.2.4. Test cases8.2.5. Summary of Section8.3. Extended-term Hybrid Simulation8.3.1. Steady-state & Dynamic Hybrid Simulation8.3.2. Extended-term Simulation Framework8.3.3. Experiments8.3.4. Summary of Section8.4. Robust Parallel or Distributed Simulation8.4.1. Steady-state contingency analysis: problem formulation and state of the art8.4.2. Partitioned holomorphic embedding (PHE)8.4.3. Parallel and Distributed Computation8.4.4. Experiment on large-scale system8.4.5. Summary of SectionIndex

O autorze

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.