| Preface | 6 |
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| Contents | 8 |
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| List of Figures | 12 |
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| List of Tables | 19 |
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| Introduction | 21 |
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| 1.1 Introduction and Definitions | 21 |
| 1.2 Historical Background of Digital Protective Relaying Algorithms | 22 |
| 1.3 Development of Protective Relaying Algorithms | 23 |
| 1.4 Introduction of Mathematical Morphology to Protective Relaying of Power Systems | 27 |
| 1.5 Contents of This Book | 30 |
| Mathematical Morphology | 33 |
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| 2.1 Introduction | 33 |
| 2.2 Basic Morphological Operators | 35 |
| 2.3 Morphological Filters | 42 |
| 2.4 The Lifting Scheme and Morphological Wavelets | 45 |
| 2.5 Summary | 57 |
| Phasor Measurement | 61 |
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| 3.1 Introduction | 61 |
| 3.2 Phasor Measurement Methods | 62 |
| 3.3 Power System Faults | 67 |
| 3.4 Morphological Transform for DC Offset Removal | 69 |
| 3.5 Results of Simulations and Discussions | 75 |
| 3.6 Summary | 76 |
| Protection of Transmission Lines | 77 |
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| 4.1 Introduction | 77 |
| 4.2 The Adaptive Distance Relaying Algorithm | 79 |
| 4.3 Implementation of ADRA | 87 |
| 4.4 Simulation Studies and Results of ADRA | 90 |
| 4.5 Protection of a Double Circuit Transmission Line | 98 |
| 4.6 The Fault Phase Selector | 99 |
| 4.7 Simulation Results and Discussions on Fault Phase Selection | 102 |
| 4.8 Summary | 109 |
| Transformer Protection | 112 |
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| 5.1 Introduction | 112 |
| 5.2 Transformer Differential Protection | 114 |
| 5.3 Transformer Magnetising Inrush | 116 |
| 5.4 Morphological Identification of Inrush | 122 |
| 5.5 Simulation Studies and Results Analysis | 128 |
| 5.6 Further Discussion of the MM-Based Schemes for Inrush Identification | 142 |
| 5.7 Summary | 143 |
| Bus Protection | 144 |
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| 6.1 Introduction | 144 |
| 6.2 Bus Differential Protection | 145 |
| 6.3 Current Transformers for Bus Protection | 145 |
| 6.4 Current Transformer Problems | 146 |
| 6.5 Saturation of Current Transformers | 148 |
| 6.6 A Morphological Lifting Scheme for Detection of CT Saturation | 149 |
| 6.7 A Compensation Algorithm for Distorted Secondary Current | 150 |
| 6.8 Case Studies | 152 |
| 6.9 Summary | 157 |
| Ultra-High-Speed Protection | 158 |
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| 7.1 Introduction | 158 |
| 7.2 Principles of UHS Protection | 160 |
| 7.3 UHS Directional Protective Relaying | 165 |
| 7.4 Summary | 179 |
| Fault Location on Transmission Lines | 183 |
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| 8.1 Introduction | 183 |
| 8.2 Principles of Fault Location | 184 |
| 8.3 Noise Removal of Transients | 191 |
| 8.4 Accurate Fault Location by Morphological Filters | 194 |
| 8.5 Morphological Undecimated Wavelet Decomposition for Fault Location | 202 |
| 8.6 Summary | 208 |
| Electromagnetic Transient Analysis of Transmission Lines | 209 |
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| A.1 Distributed Parameter Model of Transmission Lines | 209 |
| A.2 Transient Wave Propagation Characteristics | 211 |
| A.3 Incidence, Reflection and Refraction of Transients | 213 |
| References | 215 |
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| Index | 222 |