Power system simulation using semi-analytical methods / edited by Kai Sun.

Contributor(s): Sun, Kai, 1976- [editor.] | Ohio Library and Information Network
Publisher: Hoboken, New Jersey : John Wiley & Sons, Inc., [2024]Description: 1 online resource (xx, 348 pages) : illustrations (chiefly color)Content type: text Media type: computer Carrier type: online resourceISBN: 9781119988038; 1119988039; 9781119988021; 1119988020; 9781119988045; 1119988047Subject(s): Electric power systems -- Computer simulation | Electric power systems -- Simulation methods | Electric power systems -- Mathematical modelsAdditional physical formats: Print version:: Power system simulation using semi-analytical methodsDDC classification: 621.3101/13 LOC classification: TK1005 | .P7177 2024Online resources: Connect to resource | Connect to resource | Connect to resource (off-campus)
Contents:
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 Pad�e Approximants 8 -- 4.2.1 Semi-Analytical Solution Using Pad�e Approximants 8 -- 4.2.2 Pad�e 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.
Summary: "The purpose of this book is to enhance the speed of time-domain simulations of bulk power systems by introducing a semi-analytical methodology that integrates various simulation techniques. This new approach differs from traditional simulations that use low-order numerical integrators. Instead, it employs a high-order analytical form that approximates the dynamic response of the system with improved accuracy. By embedding symbolic variables and parameters, the resulting semi-analytical solution allows for the decomposition of its computation into sequential or concurrent processes, reducing the time required for simulations. Additionally, a significant amount of computation can be performed offline before a simulation run is needed or be parallelized, making the simulations even faster. These semi-analytical methods can be integrated or interfaced with existing numerical integrators to create more robust power system simulators that can be used with high-performance parallel computers. The book is structured to provide a comprehensive and systematic coverage of such emerging methods for finding semi-analytical solutions and accelerating power system simulation, as documented in literature"-- Provided by publisher.
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Includes bibliographical references and index.

"The purpose of this book is to enhance the speed of time-domain simulations of bulk power systems by introducing a semi-analytical methodology that integrates various simulation techniques. This new approach differs from traditional simulations that use low-order numerical integrators. Instead, it employs a high-order analytical form that approximates the dynamic response of the system with improved accuracy. By embedding symbolic variables and parameters, the resulting semi-analytical solution allows for the decomposition of its computation into sequential or concurrent processes, reducing the time required for simulations. Additionally, a significant amount of computation can be performed offline before a simulation run is needed or be parallelized, making the simulations even faster. These semi-analytical methods can be integrated or interfaced with existing numerical integrators to create more robust power system simulators that can be used with high-performance parallel computers. The book is structured to provide a comprehensive and systematic coverage of such emerging methods for finding semi-analytical solutions and accelerating power system simulation, as documented in literature"-- Provided by publisher.

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 Pad�e Approximants 8 -- 4.2.1 Semi-Analytical Solution Using Pad�e Approximants 8 -- 4.2.2 Pad�e 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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