Inter-area Oscillations in Power Systems (eBook)

Inter-area Oscillations in Power Systems 2
Preface 6
Acknowledgments 11
Contents 12
Contributors 13
Signal Processing Methods for Estimating Small-Signal Dynamic Properties from Measured Responses 15
1.1 Introduction 15
1.2 System Basics 16
1.3 Signal Processing Methods for Estimating Modes 19
1.3.1 Ringdown Algorithms 19
1.3.2 Mode-Meter Algorithms 21
1.4 Power System Identification Using Known Probing Signals 22
1.4.1 Probing Signal Selection 24
1.5 Mode Estimation Examples 26
1.5.1 Simulation System 27
1.5.2 Ringdown Analysis Performance 28
1.5.3 Mode-Meter Performance 29
1.5.4 Field Measured Data 33
1.5.5 Probing Test Results 34
1.6 Model Validation and Performance Assessment 38
1.6.1 Model Validation 38
1.6.2 Performance Assessment 39
1.7 Estimating Mode Shape 40
1.7.1 Defining Mode Shape 40
1.7.2 Estimating Mode Shape 41
1.7.2.1 The Coherency 42
1.7.2.2 Calculating Spectral Terms 42
1.7.3 16-Machine Example 43
1.7.4 Field Measured Data 45
1.8 Conclusion 48
References 48
Enhancements to the Hilbert-Huang Transform for Application to Power System Oscillations 51
2.1 Introduction 51
2.2 Hilbert-Huang Transform 53
2.2.1 Empirical Mode Decomposition 53
2.2.2 Hilbert Transform 54
2.3 Modified Hilbert-Huang Transform 55
2.3.1 Limitations of EMD 56
2.3.2 Masking Signal-Based EMD [5] 58
2.3.3 Frequency Heterodyne Technique [6] 59
2.4 Case Studies 62
2.4.1 Power Flow Oscillations in Large Power Systems 62
2.4.2 Torque and Field Current Variations in HTS Propulsion Motors [8] 64
2.4.3 Analyzing Slow Coherency [9] 67
2.4.4 Wide-Area Measurement Signals [9] 69
2.5 Discussion 73
2.6 Conclusion 74
References 75
Variants of Hilbert-Huang Transform with Applications to Power Systems’ Oscillatory Dynamics 76
3.1 Introduction 77
3.2 Preliminaries 78
3.2.1 Fourier Analysis 78
3.2.2 The Empirical Mode Decomposition Method 79
3.2.3 Hilbert Transform 80
3.2.4 Instantaneous Damping 81
3.2.4.1 Computation Based on the Exponential Decay 81
3.2.4.2 Computation Based on the Second-Order System Approach 82
3.2.5 Completeness, Orthogonality, and Orthogonality Index 84
3.3 Masking Techniques to Improve Empirical Mode Decomposition 85
3.3.1 The Standard EMD Method and Its Limitation 85
3.3.2 EMD Method with Fourier-Based Masking Technique 88
3.3.3 EMD Method with Energy-Based Masking Technique 91
3.3.4 Local Hilbert Transform 92
3.4 Applications 93
3.4.1 Application to a Synthetic Signal 93
3.4.1.1 Decomposing Capability Test 93
3.4.1.2 Reliability to Handle Nonlinear/Nonstationary Signals 96
3.4.2 Instantaneous Damping Computation 97
3.4.2.1 Test I 97
3.4.2.2 Test II 98
3.4.3 Application to Simulated Data 100
3.4.4 Application to Measured Data 106
3.5 Conclusion 111
References 112
Practical Application of Hilbert Transform Techniques in Identifying Inter-area Oscillations 114
4.1 Inter-area Oscillations in Power Systems 114
4.2 Present Identification Techniques 115
4.2.1 Prony Analysis 115
4.2.2 Fourier Methods 116
4.3 The Hilbert Transform and Analytic Function 119
4.3.1 Hilbert Transform Properties 119
4.3.2 Modal Parameters in Terms of the Analytic Function 120
4.3.3 Hilbert Transform Implementation 121
4.3.4 Instantaneous Frequency 122
4.4 Application to Single-Mode Signal 122
4.5 Multiple Mode Signals: Empirical Mode Decomposition 125
4.6 Factors Affecting Performance of the Technique 127
4.6.1 Modal Separation 127
4.6.2 Noise Tolerance 129
4.6.3 Changes in Underlying System Dynamics 132
4.7 Application to Physical Signals 133
4.8 Conclusions 137
References 137
A Real-Time Wide-Area Controller for Mitigating Small-Signal Instability 139
5.1 Introduction 139
5.2 The Controller 142
5.3 The Central Control Unit 143
5.3.1 Setting Up the Central Unit - Off-line Rules 145
5.3.1.1 Defining the Time Window 145
5.3.1.2 Grouping Signals by Dominant Modes 146
5.3.1.3 Using Mode Content: Group Using Ai and Ari 149
5.3.1.4 Validating the Groups 149
5.3.2 Monitoring and Control - Online Rules 151
5.3.2.1 Activation Deactivation Criteria 151
5.3.2.2 Validating Criteria 152
5.3.2.3 Selecting the SVC 153
5.3.2.4 Determining the Phase Compensation 153
5.4 The SVC Local Unit 153
5.4.1 The Classical Power System Model 154
5.4.2 The Linearized State-Space Classical Model for a Reduced Two-Area Power System 155
5.4.3 Numerical Results 158
5.4.4 SVC Rules 161
5.4.4.1 Selecting the SVC Location 162
5.4.4.2 Determining the Phase Compensation 162
5.5 WSCC Power System Example 162
5.6 Conclusions 166
References 167
Complex Empirical Orthogonal Function Analysis of Power System Oscillatory Dynamics 170
6.1 Empirical Orthogonal Function Analysis 170
6.1.1 Theoretical Development 171
6.1.2 Discrete Domain Representation 174
6.1.3 The Method of Snapshots 175
6.1.4 Energy Relationships 177
6.2 Interpretation of EOFs Using Singular Value Decomposition 178
6.2.1 Singular Value Decomposition 178
6.2.2 Relation with the Eigenvalue Decomposition 180
6.3 Numerical Computation of POMs 181
6.4 Complex Empirical Orthogonal Function Analysis 182
6.4.1 Complex EOF Analysis 184
6.4.2 Analysis of Propagating Features 185
6.5 Application to Time Synchronized Measured Data 187
6.5.1 Construction of POD Modes via the Method of Snapshots 189
6.5.2 Spatiotemporal Analysis of Measured Data 190
6.5.3 Temporal Properties 193
6.5.4 Frequency Determination from Instantaneous Phases 193
6.5.5 Mode Shape Estimation 195
6.5.6 Energy Distribution 196
6.6 Concluding Remarks and Directions for Future Research 197
References 197
Detection and Estimation of Nonstationary Power Transients 199
7.1 Introduction 199
7.2 Modal Damping Change Detection 200
7.2.1 Energy Detection Approach 201
7.2.1.1 Theory 201
7.2.1.2 PDF Derivation 201
7.2.1.3 PDF Verification 203
7.2.1.4 Results 204
7.2.2 Introduction to Kalman Approach 207
7.2.2.1 Theory (See Development in [7]) 207
7.2.2.2 Individual Mode Test Statistic Details 208
7.2.2.3 PDF Derivation 209
7.2.2.4 Results 211
7.2.3 Application to Real Data [7] 214
7.2.3.1 Part I: Analysis of the Melbourne Data 214
7.2.3.2 Part II: Combining Multisite Data for Enhanced SNR and Detection 217
7.2.3.3 Summary of Kalman Approach 221
7.3 Estimation of Modal Parameters from Nonstationary Response 221
7.3.1 Introduction 221
7.3.2 Estimation of Linear Power System Models 222
7.3.3 Time-Frequency Representations 223
7.3.4 Application to Transient Stability Swings 227
7.3.5 Error Reduction by Time-Domain Windowing 232
7.3.6 Discussion 234
7.3.7 Recommendations for Time-Frequency 237
7.4 Conclusions 237
References 238
Advanced Monitoring and Control Approaches for Enhancing Power System Security 240
8.1 Introduction 240
8.2 Monitoring Power System Oscillations by Wavelet Analysis and Wide-Area Measurements 242
8.2.1 Approaches for Monitoring Power System Oscillations 242
8.2.2 Morlet-Based Wavelet Analysis 244
8.2.3 A WAMS-Based Monitoring Architecture 247
8.2.4 Test Results A: Monitoring System Response to Small Perturbations 248
8.2.5 Test Results B: Influence of Random Fluctuations Due to Operating Conditions 252
8.2.6 Test Results C: Influence of Measurement Noise 255
8.3 Response-Based Wide-Area Control Approach 256
8.3.1 Mathematical Formulation 258
8.3.2 Test Results 262
8.3.3 Computational and Communication Time Delay Assessment 265
8.4 Conclusions 266
References 266
Index 270