Messina Inter-area Oscillations in Power Systems

A Nonlinear and Nonstationary Perspective
1. Auflage 2009
ISBN: 978-0-387-89530-7
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 275 Seiten

Reihe: Power Electronics and Power Systems

The study of complex dynamic processes governed by nonlinear and nonstationary characteristics is a problem of great importance in the analysis and control of power system oscillatory behavior. Power system dynamic processes are highly random, nonlinear to some extent, and intrinsically nonstationary even over short time intervals as in the case of severe transient oscillations in which switching events and control actions interact in a complex manner. Phenomena observed in power system oscillatory dynamics are diverse and complex. Measured ambient data are known to exhibit noisy, nonstationary fluctuations resulting primarily from small magnitude, random changes in load, driven by low-scale motions or nonlinear trends originating from slow control actions or changes in operating conditions. Forced oscillations resulting from major cascading events, on the other hand, may contain motions with a broad range of scales and can be highly nonlinear and time-varying. Prediction of temporal dynamics, with the ultimate application to real-time system monitoring, protection and control, remains a major research challenge due to the complexity of the driving dynamic and control processes operating on various temporal scales that can become dynamically involved. An understanding of system dynamics is critical for reliable inference of the underlying mechanisms in the observed oscillations and is needed for the development of effective wide-area measurement and control systems, and for improved operational reliability.

Autoren/Hrsg.

Messina, Arturo Roman

Inhaltsverzeichnis

1;Inter-area Oscillations in Power Systems;2
1.1;Preface;6
1.2;Acknowledgments;11
1.3;Contents;12
1.4;Contributors;13
1.5;Signal Processing Methods for Estimating Small-Signal Dynamic Properties from Measured Responses;15
1.5.1;1.1 Introduction;15
1.5.2;1.2 System Basics;16
1.5.3;1.3 Signal Processing Methods for Estimating Modes;19
1.5.3.1;1.3.1 Ringdown Algorithms;19
1.5.3.2;1.3.2 Mode-Meter Algorithms;21
1.5.4;1.4 Power System Identification Using Known Probing Signals;22
1.5.4.1;1.4.1 Probing Signal Selection;24
1.5.5;1.5 Mode Estimation Examples;26
1.5.5.1;1.5.1 Simulation System;27
1.5.5.2;1.5.2 Ringdown Analysis Performance;28
1.5.5.3;1.5.3 Mode-Meter Performance;29
1.5.5.4;1.5.4 Field Measured Data;33
1.5.5.5;1.5.5 Probing Test Results;34
1.5.6;1.6 Model Validation and Performance Assessment;38
1.5.6.1;1.6.1 Model Validation;38
1.5.6.2;1.6.2 Performance Assessment;39
1.5.7;1.7 Estimating Mode Shape;40
1.5.7.1;1.7.1 Defining Mode Shape;40
1.5.7.2;1.7.2 Estimating Mode Shape;41
1.5.7.2.1;1.7.2.1 The Coherency;42
1.5.7.2.2;1.7.2.2 Calculating Spectral Terms;42
1.5.7.3;1.7.3 16-Machine Example;43
1.5.7.4;1.7.4 Field Measured Data;45
1.5.8;1.8 Conclusion;48
1.5.9;References;48
1.6;Enhancements to the Hilbert-Huang Transform for Application to Power System Oscillations;51
1.6.1;2.1 Introduction;51
1.6.2;2.2 Hilbert-Huang Transform;53
1.6.2.1;2.2.1 Empirical Mode Decomposition;53
1.6.2.2;2.2.2 Hilbert Transform;54
1.6.3;2.3 Modified Hilbert-Huang Transform;55
1.6.3.1;2.3.1 Limitations of EMD;56
1.6.3.2;2.3.2 Masking Signal-Based EMD [5];58
1.6.3.3;2.3.3 Frequency Heterodyne Technique [6];59
1.6.4;2.4 Case Studies;62
1.6.4.1;2.4.1 Power Flow Oscillations in Large Power Systems;62
1.6.4.2;2.4.2 Torque and Field Current Variations in HTS Propulsion Motors [8];64
1.6.4.3;2.4.3 Analyzing Slow Coherency [9];67
1.6.4.4;2.4.4 Wide-Area Measurement Signals [9];69
1.6.5;2.5 Discussion;73
1.6.6;2.6 Conclusion;74
1.6.7;References;75
1.7;Variants of Hilbert-Huang Transform with Applications to Power Systems’ Oscillatory Dynamics;76
1.7.1;3.1 Introduction;77
1.7.2;3.2 Preliminaries;78
1.7.2.1;3.2.1 Fourier Analysis;78
1.7.2.2;3.2.2 The Empirical Mode Decomposition Method;79
1.7.2.3;3.2.3 Hilbert Transform;80
1.7.2.4;3.2.4 Instantaneous Damping;81
1.7.2.4.1;3.2.4.1 Computation Based on the Exponential Decay;81
1.7.2.4.2;3.2.4.2 Computation Based on the Second-Order System Approach;82
1.7.2.5;3.2.5 Completeness, Orthogonality, and Orthogonality Index;84
1.7.3;3.3 Masking Techniques to Improve Empirical Mode Decomposition;85
1.7.3.1;3.3.1 The Standard EMD Method and Its Limitation;85
1.7.3.2;3.3.2 EMD Method with Fourier-Based Masking Technique;88
1.7.3.3;3.3.3 EMD Method with Energy-Based Masking Technique;91
1.7.3.4;3.3.4 Local Hilbert Transform;92
1.7.4;3.4 Applications;93
1.7.4.1;3.4.1 Application to a Synthetic Signal;93
1.7.4.1.1;3.4.1.1 Decomposing Capability Test;93
1.7.4.1.2;3.4.1.2 Reliability to Handle Nonlinear/Nonstationary Signals;96
1.7.4.2;3.4.2 Instantaneous Damping Computation;97
1.7.4.2.1;3.4.2.1 Test I;97
1.7.4.2.2;3.4.2.2 Test II;98
1.7.4.3;3.4.3 Application to Simulated Data;100
1.7.4.4;3.4.4 Application to Measured Data;106
1.7.5;3.5 Conclusion;111
1.7.6;References;112
1.8;Practical Application of Hilbert Transform Techniques in Identifying Inter-area Oscillations;114
1.8.1;4.1 Inter-area Oscillations in Power Systems;114
1.8.2;4.2 Present Identification Techniques;115
1.8.2.1;4.2.1 Prony Analysis;115
1.8.2.2;4.2.2 Fourier Methods;116
1.8.3;4.3 The Hilbert Transform and Analytic Function;119
1.8.3.1;4.3.1 Hilbert Transform Properties;119
1.8.3.2;4.3.2 Modal Parameters in Terms of the Analytic Function;120
1.8.3.3;4.3.3 Hilbert Transform Implementation;121
1.8.3.4;4.3.4 Instantaneous Frequency;122
1.8.4;4.4 Application to Single-Mode Signal;122
1.8.5;4.5 Multiple Mode Signals: Empirical Mode Decomposition;125
1.8.6;4.6 Factors Affecting Performance of the Technique;127
1.8.6.1;4.6.1 Modal Separation;127
1.8.6.2;4.6.2 Noise Tolerance;129
1.8.6.3;4.6.3 Changes in Underlying System Dynamics;132
1.8.7;4.7 Application to Physical Signals;133
1.8.8;4.8 Conclusions;137
1.8.9;References;137
1.9;A Real-Time Wide-Area Controller for Mitigating Small-Signal Instability;139
1.9.1;5.1 Introduction;139
1.9.2;5.2 The Controller;142
1.9.3;5.3 The Central Control Unit;143
1.9.3.1;5.3.1 Setting Up the Central Unit - Off-line Rules;145
1.9.3.1.1;5.3.1.1 Defining the Time Window;145
1.9.3.1.2;5.3.1.2 Grouping Signals by Dominant Modes;146
1.9.3.1.3;5.3.1.3 Using Mode Content: Group Using Ai and Ari;149
1.9.3.1.4;5.3.1.4 Validating the Groups;149
1.9.3.2;5.3.2 Monitoring and Control - Online Rules;151
1.9.3.2.1;5.3.2.1 Activation Deactivation Criteria;151
1.9.3.2.2;5.3.2.2 Validating Criteria;152
1.9.3.2.3;5.3.2.3 Selecting the SVC;153
1.9.3.2.4;5.3.2.4 Determining the Phase Compensation;153
1.9.4;5.4 The SVC Local Unit;153
1.9.4.1;5.4.1 The Classical Power System Model;154
1.9.4.2;5.4.2 The Linearized State-Space Classical Model for a Reduced Two-Area Power System;155
1.9.4.3;5.4.3 Numerical Results;158
1.9.4.4;5.4.4 SVC Rules;161
1.9.4.4.1;5.4.4.1 Selecting the SVC Location;162
1.9.4.4.2;5.4.4.2 Determining the Phase Compensation;162
1.9.5;5.5 WSCC Power System Example;162
1.9.6;5.6 Conclusions;166
1.9.7;References;167
1.10;Complex Empirical Orthogonal Function Analysis of Power System Oscillatory Dynamics;170
1.10.1;6.1 Empirical Orthogonal Function Analysis;170
1.10.1.1;6.1.1 Theoretical Development;171
1.10.1.2;6.1.2 Discrete Domain Representation;174
1.10.1.3;6.1.3 The Method of Snapshots;175
1.10.1.4;6.1.4 Energy Relationships;177
1.10.2;6.2 Interpretation of EOFs Using Singular Value Decomposition;178
1.10.2.1;6.2.1 Singular Value Decomposition;178
1.10.2.2;6.2.2 Relation with the Eigenvalue Decomposition;180
1.10.3;6.3 Numerical Computation of POMs;181
1.10.4;6.4 Complex Empirical Orthogonal Function Analysis;182
1.10.4.1;6.4.1 Complex EOF Analysis;184
1.10.4.2;6.4.2 Analysis of Propagating Features;185
1.10.5;6.5 Application to Time Synchronized Measured Data;187
1.10.5.1;6.5.1 Construction of POD Modes via the Method of Snapshots;189
1.10.5.2;6.5.2 Spatiotemporal Analysis of Measured Data;190
1.10.5.3;6.5.3 Temporal Properties;193
1.10.5.4;6.5.4 Frequency Determination from Instantaneous Phases;193
1.10.5.5;6.5.5 Mode Shape Estimation;195
1.10.5.6;6.5.6 Energy Distribution;196
1.10.6;6.6 Concluding Remarks and Directions for Future Research;197
1.10.7;References;197
1.11;Detection and Estimation of Nonstationary Power Transients;199
1.11.1;7.1 Introduction;199
1.11.2;7.2 Modal Damping Change Detection;200
1.11.2.1;7.2.1 Energy Detection Approach;201
1.11.2.1.1;7.2.1.1 Theory;201
1.11.2.1.2;7.2.1.2 PDF Derivation;201
1.11.2.1.3;7.2.1.3 PDF Verification;203
1.11.2.1.4;7.2.1.4 Results;204
1.11.2.2;7.2.2 Introduction to Kalman Approach;207
1.11.2.2.1;7.2.2.1 Theory (See Development in [7]);207
1.11.2.2.2;7.2.2.2 Individual Mode Test Statistic Details;208
1.11.2.2.3;7.2.2.3 PDF Derivation;209
1.11.2.2.4;7.2.2.4 Results;211
1.11.2.3;7.2.3 Application to Real Data [7];214
1.11.2.3.1;7.2.3.1 Part I: Analysis of the Melbourne Data;214
1.11.2.3.2;7.2.3.2 Part II: Combining Multisite Data for Enhanced SNR and Detection;217
1.11.2.3.3;7.2.3.3 Summary of Kalman Approach;221
1.11.3;7.3 Estimation of Modal Parameters from Nonstationary Response;221
1.11.3.1;7.3.1 Introduction;221
1.11.3.2;7.3.2 Estimation of Linear Power System Models;222
1.11.3.3;7.3.3 Time-Frequency Representations;223
1.11.3.4;7.3.4 Application to Transient Stability Swings;227
1.11.3.5;7.3.5 Error Reduction by Time-Domain Windowing;232
1.11.3.6;7.3.6 Discussion;234
1.11.3.7;7.3.7 Recommendations for Time-Frequency;237
1.11.4;7.4 Conclusions;237
1.11.5;References;238
1.12;Advanced Monitoring and Control Approaches for Enhancing Power System Security;240
1.12.1;8.1 Introduction;240
1.12.2;8.2 Monitoring Power System Oscillations by Wavelet Analysis and Wide-Area Measurements;242
1.12.2.1;8.2.1 Approaches for Monitoring Power System Oscillations;242
1.12.2.2;8.2.2 Morlet-Based Wavelet Analysis;244
1.12.2.3;8.2.3 A WAMS-Based Monitoring Architecture;247
1.12.2.4;8.2.4 Test Results A: Monitoring System Response to Small Perturbations;248
1.12.2.5;8.2.5 Test Results B: Influence of Random Fluctuations Due to Operating Conditions;252
1.12.2.6;8.2.6 Test Results C: Influence of Measurement Noise;255
1.12.3;8.3 Response-Based Wide-Area Control Approach;256
1.12.3.1;8.3.1 Mathematical Formulation;258
1.12.3.2;8.3.2 Test Results;262
1.12.3.3;8.3.3 Computational and Communication Time Delay Assessment;265
1.12.4;8.4 Conclusions;266
1.12.5;References;266
1.13;Index;270