Offers a comprehensive introduction to the issues of control of power systems during cascading outages and restoration process
Power System Control Under Cascading Failures 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, root causes and propagation patterns of failures and power outages. Second, it covers controlled system separation to mitigate cascading failures addressing key questions such as where, when and how to separate. Third, the text explores optimal system restoration from cascading power outages and blackouts by well-designed milestones, optimised procedures and emerging techniques.
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:
Contains comprehensive coverage of a focused area of cascading power system outages, addressing modelling and analysis, system separation and power system restoration
Offers a description of theoretical models to analyse outages, methods to identify control actions to prevent propagation of outages and restore the system
Suggests state-of-the-art methods that are illustrated in detail with hands-on examples that address realistic problems to help improve current practices
Includes companion website with samples, codes and examples to support the text
Written for postgraduate students, researchers, specialists, planners and operation engineers from industry, Power System Control Under Cascading Failures contains a review of a focused area of cascading power system outages, addresses modelling and analysis, system separation, and power system restoration.
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
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KAI SUN is an Associate Professor with the Department of Electrical Engineering and Computer Science at the University of Tennessee, USA.
YUNHE HOU is an Associate Professor with the Department of Electrical and Electronic Engineering, University of Hong Kong.
WEI SUN is an Assistant Professor in the Department of Electrical and Computer Engineering of the University of Central Florida, USA.
JUNJIAN QI is an Assistant Professor in the Department of Electrical and Computer Engineering of the University of Central Florida, USA.
About the Companion Website xiii
1 Introduction 1
1.1 Importance of Modeling and Understanding Cascading Failures 1
1.1.1 Cascading Failures 1
1.1.2 Challenges in Modeling and Understanding Cascading Failures 4
1.2 Importance of Controlled System Separation 6
1.2.1 Mitigation of Cascading Failures 6
1.2.2 Uncontrolled and Controlled System Separations 7
1.3 Constructing Restoration Strategies 9
1.3.1 Importance of System Restoration 9
1.3.2 Classification of System Restoration Strategies 10
1.3.3 Challenges of System Restoration 13
1.4 Overview of the Book 15
2 Modeling of Cascading Failures 23
2.1 General Cascading Failure Models 23
2.1.1 Bak-Tang-Wiesenfeld Sandpile Model 23
2.1.2 Failure-Tolerance Sandpile Model 24
2.1.3 Motter-Lai Model 30
2.1.4 Influence Model 30
2.1.5 Binary-Decision Model 33
2.1.6 Coupled Map Lattice Model 34
2.1.7 CASCADE Model 35
2.1.8 Interdependent Failure Model 37
2.2 Power System Cascading Failure Models 39
2.2.1 Hidden Failure Model 39
2.2.2 Manchester Model 40
2.2.3 OPA Model 42
2.2.4 Improved OPA Model 46
2.2.5 OPA Model with Slow Process 49
2.2.6 AC OPA Model 58
2.2.7 Cascading Failure Models Considering Dynamics and Detailed Protections 62
3 Understanding Cascading Failures 69
3.1 Self- Organized Criticality 70
3.1.1 SOC Theory 70
3.1.2 Evidence of SOC in Blackout Data 71
3.2 Branching Processes 72
3.2.1 Definition of the Galton-Watson Branching Process 74
3.2.2 Estimation of Mean of the Offspring Distribution 74
3.2.3 Estimation of Variance of the Offspring Distribution 75
3.2.4 Processing and Discretization of Continuous Data 78
3.2.5 Estimation of Distribution of Total Outages 81
3.2.6 Statistical Insight of Branching Process Parameters 81
3.2.7 Branching Processes Applied to Line Outage Data 82
3.2.8 Branching Processes Applied to Load Shed Data 84
3.2.9 Cross-Validation for Branching Processes 85
3.2.10 Efficiency Improvement by Branching Processes 85
3.3 Multitype Branching Processes 87
3.3.1 Estimation of Multitype Branching Process Parameters 88
3.3.2 Estimation of Joint Probability Distribution of Total Outages 90
3.3.3 An Example for a Two-Type Branching Process 91
3.3.4 Validation of Estimated Joint Distribution 92
3.3.5 Number of Cascades Needed for Multitype Branching Processes 94
3.3.6 Estimated Parameters of Branching Processes 96
3.3.7 Estimated Joint Distribution of Total Outages 98
3.3.8 Cross-Validation for Multitype Branching Processes 100
3.3.9 Predicting Joint Distribution from One Type of Outage 102
3.3.10 Estimating Failure Propagation of Three Types of Outages 104
3.4 Failure Interaction Analysis 105
3.4.1 Estimation of Interactions between Component Failures 106
3.4.2 Identification of Key Links and Key Components 108
3.4.3 Interaction Model 111
3.4.4 Validation of Interaction Model 113
3.4.5 Number of Cascades Needed for Failure Interaction Analysis 115
3.4.6 Estimated Interaction Matrix and Interaction Network 119
3.4.7 Identified Key Links and Key Components 121
3.4.8 Interaction Model Validation 125
3.4.9 Cascading Failure Mitigation 129
3.4.10 Efficiency Improvement by Interaction Model 134
4 Strategies for Controlled System Separation 141
4.1 Questions to Answer 141
4.2 Literature Review 142
4.3 Constraints on Separation Points 144
4.4 Graph Models of a Power Network 148
4.4.1 Undirected Node-Weighted Graph 149
4.4.2 Directed Edge-Weighted Graph 152
4.5 Generator Grouping 153
4.5.1 Slow Coherency Analysis 154
4.5.2 Elementary Coherent Groups 158
4.6 Finding Separation Points 160
4.6.1 Formulations of the Problem 160
4.6.2 Computational Complexity 164
4.6.3 Network Reduction 167
4.6.4 Network Decomposition for Parallel Processing 173
4.6.5 Application of the Ordered Binary Decision Diagram 175
4.6.6 Checking the Transmission Capacity and Small Disruption Constraints 185
4.6.7 Checking All Constraints in Three Steps 190
5 Online Decision Support for Controlled System Separation 197
5.1 Online Decision on the Separation Strategy 197
5.1.1 Spectral Analysis-Based Method 198
5.1.2 Frequency-Amplitude Characteristics of Electromechanical Oscillation 199
5.1.3 Phase-Locked Loop-Based Method 204
5.1.4 Timing of Controlled Separation 210
5.2 WAMS- Based Unified Framework for Controlled System Separation 212
5.2.1 WAMS-Based Three-Stage CSS Scheme 212
5.2.2 Offline Analysis Stage 214
5.2.3 Online Monitoring Stage 216
5.2.4 Real-Time Control Stage 221
6 Constraints of System Restoration 225
6.1 Physical Constraints During Restoration 225
6.1.1 Generating Unit Start-Up 225
6.1.2 System Sectionalizing and Reconfiguration 230
6.1.3 Load Restoration 233
6.2 Electromagnetic Transients During System Restoration 235
6.2.1 Generator Self-Excitation 237
6.2.2 Switching Overvoltage 237
6.2.3 Resonant Overvoltage in the Case of Energizing No-Load Transformer 242
6.2.4 Impact of Magnetizing Inrush Current on Transformer 245
6.2.5 Voltage and Frequency Analysis in Picking up Load 247
7 Restoration Methodology and Implementation Algorithms 255
7.1 Algorithms for Generating Unit Start-Up 255
7.1.1 A General Bilevel Framework 255
7.1.2 Algorithms for the Primary Problem 260
7.1.3 Algorithms for the Second Problem 265
7.2 Algorithms for Load Restoration 269
7.2.1 Estimate Operational Region Bound 271
7.2.2 Formulate MINLR Model to Maximize Load Pickup 272
7.2.3 Branch-and-Cut Solver: Design and Justification 275
7.2.4 Selection of Branching Methods 278
7.3 Case Studies 278
7.3.1 Illustrative Example for Restoring Generating Units 278
7.3.2 Optimal Load Restoration Strategies for RTS 24-Bus System 283
7.3.3 Optimal Load Restoration Strategies for IEEE 118-Bus System 287
8 Renewable and Energy Storage in System Restoration 295
8.1 Planning of Renewable Generators in System Restoration 295
8.1.1 Renewables for System Restoration 295
8.1.2 The Offline Restoration Tool Using Renewable Energy Resources 296
8.1.3 System Restoration with Renewables' Participation 298
8.2 Operation and Control of Renewable Generators in System Restoration 305
8.2.1 Prerequisites of Type 3 WTs for System Restoration 307
8.2.2 Problem Setup of Type 3 WTs for System Restoration 308
8.2.3 Black-Starting Control and Sequence of Type 3 WTs 314
8.2.4 Autonomous Frequency Mechanism of a Type 3 WT-Based Stand-Alone System 317
8.2.5 Simulation Study 320
8.3 Energy Storage in System Restoration 323
8.3.1 Pumped-Storage Hydro Units in Restoration 323
8.3.2 Batteries for System Restoration 332
8.3.3 Electric Vehicles in System Restoration 340
9 Emerging Technologies in System Restoration 357
9.1 Applications of FACTS and HVDC 357
9.1.1 LCC-HVDC Technology for System Restoration 357
9.1.2 VSC-HVDC Technology for System Restoration 363
9.1.3 FACTS Technology for System Restoration 370
9.2 Applications of PMUs 376
9.2.1 Review of PMU 376
9.2.2 System Restoration with PMU Measurements 378
9.3 Microgrid in System Restoration 385
9.3.1 Microgrid-Based Restoration 385
9.3.2 Demonstration and Practice 388
10 Black-Start Capability Assessment and Optimization 399
10.1 Background of Black Start 399
10.1.1 Definition of Black Start 399
10.1.2 Constraints During BS 400
10.1.3 BS Service Procurement 401
10.1.4 Power System Restoration Procedure 403
10.2 BS Capability Assessment 404
10.2.1 Installation Criteria of New BS Generators 404
10.2.2 Optimal Installation Strategy of BS Capability 407
10.2.3 Examples 408
10.3 Optimal BS Capability 411
10.3.1 Problem Formulation 411
10.3.2 Solution Algorithm 418
10.3.3 Examples 421
1.1 Importance of Modeling and Understanding Cascading Failures
1.1.1 Cascading Failures
Cascading failures can happen in many different systems, such as in electric power systems [1-7], the Internet , the road system , and in social and economic systems . These low-probability high-impact events can produce significant economic and social losses.
In electric power grids, cascading blackouts are complicated sequences of dependent outages that could bring about tremendous economic and social losses. Large-scale cascading blackouts have substantial risk and pose great challenges in simulation, analysis, and mitigation. It is important to study the mechanisms of cascading failures so that the risk of large-scale blackouts may be better quantified and mitigated. Cascading blackouts are usually considered rare events, but they are not that uncommon. The frequency of these high-impact events is not as low as expected. The following is a subset of the very famous large-scale blackouts around the world.
- 1965 Northeast blackout: There was a significant disruption in the supply of electricity on November 9, 1965, affecting parts of Ontario in Canada and Connecticut, Massachusetts, New Hampshire, New Jersey, New York, Rhode Island, Pennsylvania, and Vermont in the United States. Over 30 million people and 80,000 square miles were left without electricity for up to 13?hours .
- 1996 Western North America blackouts: A disturbance occurred on July 2, 1996, which ultimately resulted in the Western Systems Coordinating Council () system separating into five islands and in electric service interruptions to over two million customers. Electric service was restored to most customers within 30?minutes, except on the Idaho Power Company () system, a portion of the Public Service Company of Colorado (), and the Platte River Power Authority () systems in Colorado, where some customers were out of service for up to 6 hours . The first significant event was a single phase-to-ground fault on the 345-kV Jim Bridger-Kinport line due to a flashover (arc) when the conductor sagged close to a tree. On July 3, a similar blackout occurred, also initiated by the tree flashover of the 345?kV Jim Bridger-Kinport line.
- 2003 U.S.-Canadian blackout: A widespread power outage occurred throughout parts of the northeastern and midwestern United States and the Canadian province of Ontario on August 14, 2003, affecting an estimated 10 million people in Ontario and 45 million people in eight U.S. states . The initiating events were the out-of-service of a generating plant in Eastlake, Ohio, and the following tripping of several transmission lines due to tree flashover. Key factors include inoperative state estimator due to incorrect telemetry data and the failure of the alarm system at FirstEnergy's control room.
- 2003 Italy blackout: There was a serious power outage that affected all of Italy - except the islands of Sardinia and Elba - for 12?hours and part of Switzerland near Geneva for 3?hours on September 28, 2003. It was the largest blackout in the series of blackouts in 2003, affecting a total of 56 million people . The initiating event was the tripping of a major tie line from Switzerland to Italy due to tree flashover. Then a second 380-kV line also tripped on the same border (Italy-Switzerland) due to tree contact. The resulting power deficit in Italy caused Italy to lose synchronism with the rest of Europe, and the lines on the interface between France and Italy were tripped by distance relays. The same happened for the 220-kV interconnection between Italy and Austria. Subsequently, the final 380-kV corridor between Italy and Slovenia became overloaded and it too was tripped. Due to a significant amount of power shortage, the frequency in the Italian system started to fall. The frequency decay was not controlled adequately to stop generation from tripping due to underfrequency. Thus, over the course of several minutes, the entire Italian system collapsed, causing a nationwide blackout .
- 2012 Indian blackout: On July 30 and 31, 2012, there was a major blackout in India that affected over 600 million people. On July 30, nearly the entire north region covering eight states was affected, with a loss of 38?000?MW of load. On July 31, 48?000?MW of load was shed, affecting 21 states. These major failures in the synchronously operating North-East-Northeast-West grid were initiated by overloadin of an interregional tie line on both days [16-18].
- 2015 Ukrainian blackout: On December 23, 2015, the Ukrainian Kyivoblenergo, a regional electricity distribution company, reported service outages to customers . The outages were due to a third party's illegal entry into the company's computer and supervisory control and data acquisition () systems: Starting at approximately 3:35?p.m. local time, seven 110-kV and 23 35-kV substations were disconnected for 3 hours. Later statements indicated that the cyber-attack impacted additional portions of the distribution grid and forced operators to switch to manual mode. The event was elaborated on by the Ukrainian news media, who conducted interviews and determined that a foreign attacker remotely controlled the distribution management system. The outages were originally thought to have affected approximately 80,000 customers, based on the Kyivoblenergo's update to customers. However, later it was revealed that three different distribution companies were attacked, resulting in several outages that caused approximately 225,000 customers to lose power across various areas.
- 2016 Southern California disturbance: On August 16, 2016, the Blue Cut fire began in the Cajon Pass and quickly moved toward an important transmission corridor that is composed of three 500-kV lines owned by Southern California Edison () and two 287-kV lines owned by Los Angeles Department of Water and Power () . The transmission system experienced 13 500-kV line faults, and the system experienced two 287-kV faults because of the fire. Four of these fault events resulted in the loss of a significant amount of solar photovoltaic () generation. The most significant event related to the solar generation loss occurred at 11:45?a.m. Pacific Time and resulted in the loss of nearly 1200?MW.
- 2016 South Australia (SA) blackout: On September 28, 2016 there was a widespread power outage in SA power grid which caused around 850,000 customers to lose their power supply . Before the blackout the total load including loss in the SA power grid was 1826 MW, among which around 883 MW was supplied by wind generation, corresponding to a very high renewable penetration . Late in the afternoon a severe storm hit SA and damaged several remote transmission towers. The SA grid subsequently lost around 52% of wind generation within a few minutes. This deficit had to be compensated by the power import from the neighboring state, Victoria, through the Heywood AC interconnection. The significantly increased power flow was beyond the capability of the interconnection. Ultimately the SA system was separated from the rest of the system before it collapsed .
Some of the past cascading blackouts share similarities. For example, the two significant outages in the western North America in 1996 , the U.S.-Canadian blackout on August 14, 2003 , and the outage in Italy on September 28, 2003 , all had tree contact with transmission lines . Modeling and understanding these common features will help prevent future cascading blackouts that might be initiated by the same reason. At the same time, each blackout has its own unique features due to the characteristics of the particular system, which makes the modeling and understanding of cascading failures challenging.
1.1.2 Challenges in Modeling and Understanding Cascading Failures
The modeling and understanding of cascading failures, or in particular cascading blackouts, can be very challenging in the following aspects:
- Size of the system: The size of the interconnected power system can be very large. For example, in the United States utility companies build power system models, which are then used to create the North American Electric Reliability Corporation () interconnection-wide models, with over 50?000 buses. Modeling and understanding the possible ways that such a big system fails can be really challenging.
- Limited computational power: The computational power is constantly improving as technologies for both hardware and software advance. However, it is still very limited. Although N?-?1 contingency analysis is usually achievable, even only N?-?2 contingency analysis for a system with thousands of components can lead to formidable computational burden .
- Mechanisms in cascading blackouts: There can be many mechanisms during a cascading blackout, which can include thermal dynamics of the...
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