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<p>About the Companion Website xiii</p> <p><b>1 Introduction </b><b>1</b></p> <p>1.1 Importance of Modeling and Understanding Cascading Failures 1</p> <p>1.1.1 Cascading Failures 1</p> <p>1.1.2 Challenges in Modeling and Understanding Cascading Failures 4</p> <p>1.2 Importance of Controlled System Separation 6</p> <p>1.2.1 Mitigation of Cascading Failures 6</p> <p>1.2.2 Uncontrolled and Controlled System Separations 7</p> <p>1.3 Constructing Restoration Strategies 9</p> <p>1.3.1 Importance of System Restoration 9</p> <p>1.3.2 Classification of System Restoration Strategies 10</p> <p>1.3.3 Challenges of System Restoration 13</p> <p>1.4 Overview of the Book 15</p> <p>References 18</p> <p><b>2 Modeling of Cascading Failures </b><b>23</b></p> <p>2.1 General Cascading Failure Models 23</p> <p>2.1.1 Bak–Tang–Wiesenfeld Sandpile Model 23</p> <p>2.1.2 Failure‐Tolerance Sandpile Model 24</p> <p>2.1.3 Motter–Lai Model 30</p> <p>2.1.4 Influence Model 30</p> <p>2.1.5 Binary‐Decision Model 33</p> <p>2.1.6 Coupled Map Lattice Model 34</p> <p>2.1.7 CASCADE Model 35</p> <p>2.1.8 Interdependent Failure Model 37</p> <p>2.2 Power System Cascading Failure Models 39</p> <p>2.2.1 Hidden Failure Model 39</p> <p>2.2.2 Manchester Model 40</p> <p>2.2.3 OPA Model 42</p> <p>2.2.4 Improved OPA Model 46</p> <p>2.2.5 OPA Model with Slow Process 49</p> <p>2.2.6 AC OPA Model 58</p> <p>2.2.7 Cascading Failure Models Considering Dynamics and Detailed Protections 62</p> <p>References 64</p> <p><b>3 Understanding Cascading Failures </b><b>69</b></p> <p>3.1 Self‐ Organized Criticality 70</p> <p>3.1.1 SOC Theory 70</p> <p>3.1.2 Evidence of SOC in Blackout Data 71</p> <p>3.2 Branching Processes 72</p> <p>3.2.1 Definition of the Galton–Watson Branching Process 74</p> <p>3.2.2 Estimation of Mean of the Offspring Distribution 74</p> <p>3.2.3 Estimation of Variance of the Offspring Distribution 75</p> <p>3.2.4 Processing and Discretization of Continuous Data 78</p> <p>3.2.5 Estimation of Distribution of Total Outages 81</p> <p>3.2.6 Statistical Insight of Branching Process Parameters 81</p> <p>3.2.7 Branching Processes Applied to Line Outage Data 82</p> <p>3.2.8 Branching Processes Applied to Load Shed Data 84</p> <p>3.2.9 Cross‐Validation for Branching Processes 85</p> <p>3.2.10 Efficiency Improvement by Branching Processes 85</p> <p>3.3 Multitype Branching Processes 87</p> <p>3.3.1 Estimation of Multitype Branching Process Parameters 88</p> <p>3.3.2 Estimation of Joint Probability Distribution of Total Outages 90</p> <p>3.3.3 An Example for a Two‐Type Branching Process 91</p> <p>3.3.4 Validation of Estimated Joint Distribution 92</p> <p>3.3.5 Number of Cascades Needed for Multitype Branching Processes 94</p> <p>3.3.6 Estimated Parameters of Branching Processes 96</p> <p>3.3.7 Estimated Joint Distribution of Total Outages 98</p> <p>3.3.8 Cross‐Validation for Multitype Branching Processes 100</p> <p>3.3.9 Predicting Joint Distribution from One Type of Outage 102</p> <p>3.3.10 Estimating Failure Propagation of Three Types of Outages 104</p> <p>3.4 Failure Interaction Analysis 105</p> <p>3.4.1 Estimation of Interactions between Component Failures 106</p> <p>3.4.2 Identification of Key Links and Key Components 108</p> <p>3.4.3 Interaction Model 111</p> <p>3.4.4 Validation of Interaction Model 113</p> <p>3.4.5 Number of Cascades Needed for Failure Interaction Analysis 115</p> <p>3.4.6 Estimated Interaction Matrix and Interaction Network 119</p> <p>3.4.7 Identified Key Links and Key Components 121</p> <p>3.4.8 Interaction Model Validation 125</p> <p>3.4.9 Cascading Failure Mitigation 129</p> <p>3.4.10 Efficiency Improvement by Interaction Model 134</p> <p>References 137</p> <p><b>4 Strategies for Controlled System Separation </b><b>141</b></p> <p>4.1 Questions to Answer 141</p> <p>4.2 Literature Review 142</p> <p>4.3 Constraints on Separation Points 144</p> <p>4.4 Graph Models of a Power Network 148</p> <p>4.4.1 Undirected Node‐Weighted Graph 149</p> <p>4.4.2 Directed Edge‐Weighted Graph 152</p> <p>4.5 Generator Grouping 153</p> <p>4.5.1 Slow Coherency Analysis 154</p> <p>4.5.2 Elementary Coherent Groups 158</p> <p>4.6 Finding Separation Points 160</p> <p>4.6.1 Formulations of the Problem 160</p> <p>4.6.2 Computational Complexity 164</p> <p>4.6.3 Network Reduction 167</p> <p>4.6.4 Network Decomposition for Parallel Processing 173</p> <p>4.6.5 Application of the Ordered Binary Decision Diagram 175</p> <p>4.6.6 Checking the Transmission Capacity and Small Disruption Constraints 185</p> <p>4.6.7 Checking All Constraints in Three Steps 190</p> <p>References 192</p> <p><b>5 Online Decision Support for Controlled System Separation </b><b>197</b></p> <p>5.1 Online Decision on the Separation Strategy 197</p> <p>5.1.1 Spectral Analysis-Based Method 198</p> <p>5.1.2 Frequency‐Amplitude Characteristics of Electromechanical Oscillation 199</p> <p>5.1.3 Phase‐Locked Loop-Based Method 204</p> <p>5.1.4 Timing of Controlled Separation 210</p> <p>5.2 WAMS‐ Based Unified Framework for Controlled System Separation 212</p> <p>5.2.1 WAMS‐Based Three‐Stage CSS Scheme 212</p> <p>5.2.2 Offline Analysis Stage 214</p> <p>5.2.3 Online Monitoring Stage 216</p> <p>5.2.4 Real‐Time Control Stage 221</p> <p>References 223</p> <p><b>6 Constraints of System Restoration </b><b>225</b></p> <p>6.1 Physical Constraints During Restoration 225</p> <p>6.1.1 Generating Unit Start‐Up 225</p> <p>6.1.2 System Sectionalizing and Reconfiguration 230</p> <p>6.1.3 Load Restoration 233</p> <p>6.2 Electromagnetic Transients During System Restoration 235</p> <p>6.2.1 Generator Self‐Excitation 237</p> <p>6.2.2 Switching Overvoltage 237</p> <p>6.2.3 Resonant Overvoltage in the Case of Energizing No‐Load Transformer 242</p> <p>6.2.4 Impact of Magnetizing Inrush Current on Transformer 245</p> <p>6.2.5 Voltage and Frequency Analysis in Picking up Load 247</p> <p>References 251</p> <p><b>7 Restoration Methodology and Implementation Algorithms </b><b>255</b></p> <p>7.1 Algorithms for Generating Unit Start‐Up 255</p> <p>7.1.1 A General Bilevel Framework 255</p> <p>7.1.2 Algorithms for the Primary Problem 260</p> <p>7.1.3 Algorithms for the Second Problem 265</p> <p>7.2 Algorithms for Load Restoration 269</p> <p>7.2.1 Estimate Operational Region Bound 271</p> <p>7.2.2 Formulate MINLR Model to Maximize Load Pickup 272</p> <p>7.2.3 Branch‐and‐Cut Solver: Design and Justification 275</p> <p>7.2.4 Selection of Branching Methods 278</p> <p>7.3 Case Studies 278</p> <p>7.3.1 Illustrative Example for Restoring Generating Units 278</p> <p>7.3.2 Optimal Load Restoration Strategies for RTS 24‐Bus System 283</p> <p>7.3.3 Optimal Load Restoration Strategies for IEEE 118‐Bus System 287</p> <p>References 291</p> <p><b>8 Renewable and Energy Storage in System Restoration </b><b>295</b></p> <p>8.1 Planning of Renewable Generators in System Restoration 295</p> <p>8.1.1 Renewables for System Restoration 295</p> <p>8.1.2 The Offline Restoration Tool Using Renewable Energy Resources 296</p> <p>8.1.3 System Restoration with Renewables’ Participation 298</p> <p>8.2 Operation and Control of Renewable Generators in System Restoration 305</p> <p>8.2.1 Prerequisites of Type 3 WTs for System Restoration 307</p> <p>8.2.2 Problem Setup of Type 3 WTs for System Restoration 308</p> <p>8.2.3 Black‐Starting Control and Sequence of Type 3 WTs 314</p> <p>8.2.4 Autonomous Frequency Mechanism of a Type 3 WT-Based Stand‐Alone System 317</p> <p>8.2.5 Simulation Study 320</p> <p>8.3 Energy Storage in System Restoration 323</p> <p>8.3.1 Pumped‐Storage Hydro Units in Restoration 323</p> <p>8.3.2 Batteries for System Restoration 332</p> <p>8.3.3 Electric Vehicles in System Restoration 340</p> <p>References 351</p> <p><b>9 Emerging Technologies in System Restoration </b><b>357</b></p> <p>9.1 Applications of FACTS and HVDC 357</p> <p>9.1.1 LCC‐HVDC Technology for System Restoration 357</p> <p>9.1.2 VSC‐HVDC Technology for System Restoration 363</p> <p>9.1.3 FACTS Technology for System Restoration 370</p> <p>9.2 Applications of PMUs 376</p> <p>9.2.1 Review of PMU 376</p> <p>9.2.2 System Restoration with PMU Measurements 378</p> <p>9.3 Microgrid in System Restoration 385</p> <p>9.3.1 Microgrid‐Based Restoration 385</p> <p>9.3.2 Demonstration and Practice 388</p> <p>References 393</p> <p><b>10 Black-Start Capability Assessment and Optimization </b><b>399</b></p> <p>10.1 Background of Black Start 399</p> <p>10.1.1 Definition of Black Start 399</p> <p>10.1.2 Constraints During BS 400</p> <p>10.1.3 BS Service Procurement 401</p> <p>10.1.4 Power System Restoration Procedure 403</p> <p>10.2 BS Capability Assessment 404</p> <p>10.2.1 Installation Criteria of New BS Generators 404</p> <p>10.2.2 Optimal Installation Strategy of BS Capability 407</p> <p>10.2.3 Examples 408</p> <p>10.3 Optimal BS Capability 411</p> <p>10.3.1 Problem Formulation 411</p> <p>10.3.2 Solution Algorithm 418</p> <p>10.3.3 Examples 421</p> <p>References 431</p> <p>Index 433</p>

<p><b>KAI SUN</b> is an Associate Professor with the Department of Electrical Engineering and Computer Science at the University of Tennessee, USA. <p><b>YUNHE HOU</b> is an Associate Professor with the Department of Electrical and Electronic Engineering, University of Hong Kong. <p><b>WEI SUN</b> is an Assistant Professor in the Department of Electrical and Computer Engineering of the University of Central Florida, USA. <p><b>JUNJIAN QI</b> is an Assistant Professor in the Department of Electrical and Computer Engineering of the University of Central Florida, USA.

<p>OFFERS A COMPREHENSIVE INTRODUCTION TO THE ISSUES OF CONTROL OF POWER SYSTEMS DURING CASCADING OUTAGES AND RESTORATION PROCESS <p><i>Power System Control Under Cascading Failures</i> offers comprehensive coverage of three major topics related to prevention of cascading power outages in a power transmission grid: modelling and analysis, system separation and power system restoration. The book examines modelling and analysis of cascading failures for reliable and efficient simulation and better understanding of important mechanisms, as well as root causes and propagation patterns of failures and power outages. It also covers controlled system separation to mitigate cascading failures addressing key questions such as where, when and how to separate. The text explores optimal system restoration from cascading power outages and blackouts by well-designed milestones, optimised procedures and emerging techniques. <p>The authors — noted experts in the field — include state-of-the-art methods that are illustrated in detail as well as practical examples that show how to use them to address realistic problems and improve current practices. This important resource: <ul> <li>Contains comprehensive coverage of a focused area of cascading power system outages, addressing modelling and analysis, system separation and power system restoration</li> <li>Offers a description of theoretical models to analyse outages, methods to identify control actions to prevent propagation of outages and restore the system</li> <li>Suggests state-of-the-art methods that are illustrated in detail with hands-on examples that address realistic problems to help improve current practices</li> <li>Includes companion website with samples, codes and examples to support the text</li> </ul> <p>Written for postgraduate students, researchers, specialists, planners and operation engineers from industry, <i>Power System Control Under Cascading Failures</i> contains a review of a focused area of cascading power system outages, addresses modelling and analysis, system separation, and power system restoration

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