{"product_id":"optimal-coordination-of-power-protective-devices-with-illustrative-examples-9781119794851","title":"Optimal Coordination of Power Protective Devices","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOptimal Coordination of Power Protective Devices with Illustrative Examples Provides practical guidance on the coordination issue of power protective relays and fuses Protecting electrical power systems requires devices that isolate the components that are under fault while keeping the rest of the system stable. Optimal Coordination of Power Protective Devices with Illustrative Examples provides a thorough introduction to the optimal coordination of power systems protection using fuses and protective relays. Integrating fundamental theory and real-world practice, the text begins with an overview of power system protection and optimization, followed by a systematic description of the essential steps in designing optimal coordinators using only directional overcurrent relays. Subsequent chapters present mathematical formulations for solving many standard test systems, and cover a variety of popular hybrid optimization schemes and their mechanisms. The author also discusses a selection of\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAuthor Biography xvi\u003c\/p\u003e \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003eAcknowledgments xviii\u003c\/p\u003e \u003cp\u003eAcronyms xix\u003c\/p\u003e \u003cp\u003eAbout The Companion Website xxiii\u003c\/p\u003e \u003cp\u003eIntroduction xxv\u003cbr\u003e \u003cb\u003e1 Fundamental Steps in Optimization Algorithms 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Overview 1\u003c\/p\u003e \u003cp\u003e1.1.1 Design Variables 4\u003c\/p\u003e \u003cp\u003e1.1.2 Design Parameters 4\u003c\/p\u003e \u003cp\u003e1.1.3 Design Function 5\u003c\/p\u003e \u003cp\u003e1.1.4 Objective Function(s) 5\u003c\/p\u003e \u003cp\u003e1.1.5 Design Constraints 7\u003c\/p\u003e \u003cp\u003e1.1.5.1 Mathematical Constraints 8\u003c\/p\u003e \u003cp\u003e1.1.5.2 Inequality Constraints 8\u003c\/p\u003e \u003cp\u003e1.1.5.3 Side Constraints 9\u003c\/p\u003e \u003cp\u003e1.1.6 General Principles 10\u003c\/p\u003e \u003cp\u003e1.1.6.1 Feasible Space vs. Search Space 10\u003c\/p\u003e \u003cp\u003e1.1.6.2 Global Optimum vs. Local Optimum 11\u003c\/p\u003e \u003cp\u003e1.1.6.3 Types of Problem 12\u003c\/p\u003e \u003cp\u003e1.1.7 Standard Format 12\u003c\/p\u003e \u003cp\u003e1.1.8 Constraint-Handling Techniques 13\u003c\/p\u003e \u003cp\u003e1.1.8.1 Random Search Method 17\u003c\/p\u003e \u003cp\u003e1.1.8.2 Constant Penalty Function 17\u003c\/p\u003e \u003cp\u003e1.1.8.3 Binary Static Penalty Function 18\u003c\/p\u003e \u003cp\u003e1.1.8.4 Superiority of Feasible Points (SFPs) – Type I 18\u003c\/p\u003e \u003cp\u003e1.1.8.5 Superiority of Feasible Points (sfp) – Type II 18\u003c\/p\u003e \u003cp\u003e1.1.8.6 Eclectic Evolutionary Algorithm 18\u003c\/p\u003e \u003cp\u003e1.1.8.7 Typical Dynamic Penalty Function 19\u003c\/p\u003e \u003cp\u003e1.1.8.8 Exponential Dynamic Penalty Function 19\u003c\/p\u003e \u003cp\u003e1.1.8.9 Adaptive Multiplication Penalty Function 19\u003c\/p\u003e \u003cp\u003e1.1.8.10 Self-Adaptive Penalty Function (SAPF) 20\u003c\/p\u003e \u003cp\u003e1.1.9 Performance Criteria Used to Evaluate Algorithms 21\u003c\/p\u003e \u003cp\u003e1.1.10 Types of Optimization Techniques 23\u003c\/p\u003e \u003cp\u003e1.2 Classical Optimization Algorithms 23\u003c\/p\u003e \u003cp\u003e1.2.1 Linear Programming 25\u003c\/p\u003e \u003cp\u003e1.2.1.1 Historical Time-Line 25\u003c\/p\u003e \u003cp\u003e1.2.1.2 Mathematical Formulation of LP Problems 26\u003c\/p\u003e \u003cp\u003e1.2.1.3 Linear Programming Solvers 26\u003c\/p\u003e \u003cp\u003e1.2.2 Global-Local Optimization Strategy 28\u003c\/p\u003e \u003cp\u003e1.2.2.1 Multi-Start Linear Programming 29\u003c\/p\u003e \u003cp\u003e1.2.2.2 Hybridizing LP with Meta-Heuristic Optimization Algorithms as a Fine-Tuning Unit 31\u003c\/p\u003e \u003cp\u003e1.3 Meta-Heuristic Algorithms 33\u003c\/p\u003e \u003cp\u003e1.3.1 Biogeography-Based Optimization 34\u003c\/p\u003e \u003cp\u003e1.3.1.1 Migration Stage 40\u003c\/p\u003e \u003cp\u003e1.3.1.2 Mutation Stage 41\u003c\/p\u003e \u003cp\u003e1.3.1.3 Clear Duplication Stage 43\u003c\/p\u003e \u003cp\u003e1.3.1.4 Elitism Stage 44\u003c\/p\u003e \u003cp\u003e1.3.1.5 The Overall BBO Algorithm 45\u003c\/p\u003e \u003cp\u003e1.3.2 Differential Evolution 45\u003c\/p\u003e \u003cp\u003e1.4 Hybrid Optimization Algorithms 46\u003c\/p\u003e \u003cp\u003e1.4.1 Bbo-lp 48\u003c\/p\u003e \u003cp\u003e1.4.2 Bbo\/de 51\u003c\/p\u003e \u003cp\u003eProblems 51\u003c\/p\u003e \u003cp\u003eWritten Exercises 51\u003c\/p\u003e \u003cp\u003eComputer Exercises 53\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Fundamentals of Power System Protection 57\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Faults Classification 57\u003c\/p\u003e \u003cp\u003e2.2 Protection System 61\u003c\/p\u003e \u003cp\u003e2.3 Zones of Protection 65\u003c\/p\u003e \u003cp\u003e2.4 Primary and Backup Protection 66\u003c\/p\u003e \u003cp\u003e2.5 Performance and Design Criteria 66\u003c\/p\u003e \u003cp\u003e2.5.1 Reliability 66\u003c\/p\u003e \u003cp\u003e2.5.1.1 Dependability 66\u003c\/p\u003e \u003cp\u003e2.5.1.2 Security 66\u003c\/p\u003e \u003cp\u003e2.5.2 Sensitivity 67\u003c\/p\u003e \u003cp\u003e2.5.3 Speed 67\u003c\/p\u003e \u003cp\u003e2.5.4 Selectivity 67\u003c\/p\u003e \u003cp\u003e2.5.5 Performance versus Economics 67\u003c\/p\u003e \u003cp\u003e2.5.6 Adequateness 67\u003c\/p\u003e \u003cp\u003e2.5.7 Simplicity 67\u003c\/p\u003e \u003cp\u003e2.6 Overcurrent Protective Devices 67\u003c\/p\u003e \u003cp\u003e2.6.1 Fuses 68\u003c\/p\u003e \u003cp\u003e2.6.2 Bimetallic Relays 69\u003c\/p\u003e \u003cp\u003e2.6.3 Overcurrent Protective Relays 69\u003c\/p\u003e \u003cp\u003e2.6.4 Instantaneous OCR (IOCR) 70\u003c\/p\u003e \u003cp\u003e2.6.5 Definite Time OCR (DTOCR) 71\u003c\/p\u003e \u003cp\u003e2.6.6 Inverse Time OCR (ITOCR) 72\u003c\/p\u003e \u003cp\u003e2.6.7 Mixed Characteristic Curves 73\u003c\/p\u003e \u003cp\u003e2.6.7.1 Definite-Time Plus Instantaneous 73\u003c\/p\u003e \u003cp\u003e2.6.7.2 Inverse-Time Plus Instantaneous 74\u003c\/p\u003e \u003cp\u003e2.6.7.3 Inverse-Time Plus Definite-Time Plus Instantaneous 74\u003c\/p\u003e \u003cp\u003e2.6.7.4 Inverse-Time Plus Definite-Time 75\u003c\/p\u003e \u003cp\u003e2.6.7.5 Inverse Definite Minimum Time (IDMT) 76\u003c\/p\u003e \u003cp\u003eProblems 76\u003c\/p\u003e \u003cp\u003eWritten Exercises 76\u003c\/p\u003e \u003cp\u003eComputer Exercises 77\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Mathematical Modeling of Inverse-Time Overcurrent Relay Characteristics 79\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Computer Representation of Inverse-Time Overcurrent Relay Characteristics 79\u003c\/p\u003e \u003cp\u003e3.1.1 Direct Data Storage 79\u003c\/p\u003e \u003cp\u003e3.1.2 Curve Fitting Formulas 82\u003c\/p\u003e \u003cp\u003e3.1.2.1 Polynomial Equations 82\u003c\/p\u003e \u003cp\u003e3.1.2.2 Exponential Equations 89\u003c\/p\u003e \u003cp\u003e3.1.2.3 Artificial Intelligence 93\u003c\/p\u003e \u003cp\u003e3.1.3 Special Models 94\u003c\/p\u003e \u003cp\u003e3.1.3.1 RI-Type Characteristic 94\u003c\/p\u003e \u003cp\u003e3.1.3.2 RD-Type Characteristic 95\u003c\/p\u003e \u003cp\u003e3.1.3.3 FR Short Time Inverse 95\u003c\/p\u003e \u003cp\u003e3.1.3.4 UK Rectifier Protection 95\u003c\/p\u003e \u003cp\u003e3.1.3.5 BNP-Type Characteristic 95\u003c\/p\u003e \u003cp\u003e3.1.3.6 Standard CO Series Characteristics 95\u003c\/p\u003e \u003cp\u003e3.1.3.7 IAC and ANSI Special Equations 96\u003c\/p\u003e \u003cp\u003e3.1.4 User-Defined Curves 98\u003c\/p\u003e \u003cp\u003e3.2 Dealing with All the Standard Characteristic Curves Together 99\u003c\/p\u003e \u003cp\u003e3.2.1 Differentiating Between Time Dial Setting and Time Multiplier Setting 99\u003c\/p\u003e \u003cp\u003e3.2.2 Dealing with Time Dial Setting and Time Multiplier Setting as One Variable 104\u003c\/p\u003e \u003cp\u003e3.2.2.1 Fixed Divisor 106\u003c\/p\u003e \u003cp\u003e3.2.2.2 Linear Interpolation 108\u003c\/p\u003e \u003cp\u003e3.2.3 General Guidelines Before Conducting Researches and Studies 111\u003c\/p\u003e \u003cp\u003eProblems 113\u003c\/p\u003e \u003cp\u003eWritten Exercises 113\u003c\/p\u003e \u003cp\u003eComputer Exercises 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Upper Limit of Relay Operating Time 117\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Do We Need to Define T max ? 117\u003c\/p\u003e \u003cp\u003e4.2 How to Define T max ? 118\u003c\/p\u003e \u003cp\u003e4.2.1 Thermal Equations 118\u003c\/p\u003e \u003cp\u003e4.2.1.1 Thermal Overload Protection for 3φ Overhead Lines and Cables 118\u003c\/p\u003e \u003cp\u003e4.2.1.2 Thermal Overload Protection for Motors 122\u003c\/p\u003e \u003cp\u003e4.2.1.3 Thermal Overload Protection for Transformers 124\u003c\/p\u003e \u003cp\u003e4.2.2 Stability Analysis 126\u003c\/p\u003e \u003cp\u003eProblems 136\u003c\/p\u003e \u003cp\u003eWritten Exercises 136\u003c\/p\u003e \u003cp\u003eComputer Exercises 138\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Directional Overcurrent Relays and the Importance of Relay Coordination 139\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Relay Grading in Radial Systems 139\u003c\/p\u003e \u003cp\u003e5.1.1 Time Grading 140\u003c\/p\u003e \u003cp\u003e5.1.2 Current Grading 140\u003c\/p\u003e \u003cp\u003e5.1.3 Inverse-Time Grading 143\u003c\/p\u003e \u003cp\u003e5.2 Directional Overcurrent Relays 146\u003c\/p\u003e \u003cp\u003e5.3 Coordination of DOCRs 148\u003c\/p\u003e \u003cp\u003e5.4 Is the Coordination of DOCRs an Iterative Problem? 148\u003c\/p\u003e \u003cp\u003e5.5 Minimum Break-Point Set 161\u003c\/p\u003e \u003cp\u003e5.6 Summary 163\u003c\/p\u003e \u003cp\u003eProblems 164\u003c\/p\u003e \u003cp\u003eWritten Exercises 164\u003c\/p\u003e \u003cp\u003eComputer Exercises 166\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 General Mechanism to Optimally Coordinate Directional Overcurrent Relays 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Constructing Power Network 169\u003c\/p\u003e \u003cp\u003e6.2 Power Flow Analysis 170\u003c\/p\u003e \u003cp\u003e6.2.1 Per-Unit System and Three-to-One-Phase Conversion 172\u003c\/p\u003e \u003cp\u003e6.2.2 Power Flow Solvers 173\u003c\/p\u003e \u003cp\u003e6.2.3 How to Apply the Newton–Raphson Method 175\u003c\/p\u003e \u003cp\u003e6.2.4 Sparsity Effect 179\u003c\/p\u003e \u003cp\u003e6.3 P\/B Pairs Identification 186\u003c\/p\u003e \u003cp\u003e6.3.1 Inspection Method 186\u003c\/p\u003e \u003cp\u003e6.3.2 Graph Theory Methods 186\u003c\/p\u003e \u003cp\u003e6.3.3 Special Software 188\u003c\/p\u003e \u003cp\u003e6.4 Short-Circuit Analysis 189\u003c\/p\u003e \u003cp\u003e6.4.1 Short-Circuit Calculations 189\u003c\/p\u003e \u003cp\u003e6.4.2 Electric Power Engineering Software Tools 190\u003c\/p\u003e \u003cp\u003e6.4.2.1 Minimum Short-Circuit Current 190\u003c\/p\u003e \u003cp\u003e6.4.2.2 Maximum Short-Circuit Current 192\u003c\/p\u003e \u003cp\u003e6.4.3 Most Popular Standards 193\u003c\/p\u003e \u003cp\u003e6.4.3.1 ANSI\/IEEE Standards C37 \u0026amp; UL 489 193\u003c\/p\u003e \u003cp\u003e6.4.3.2 IEC 61363 Standard 194\u003c\/p\u003e \u003cp\u003e6.4.3.3 IEC 60909 Standard 194\u003c\/p\u003e \u003cp\u003e6.5 Applying Optimization Techniques 201\u003c\/p\u003e \u003cp\u003eProblems 202\u003c\/p\u003e \u003cp\u003eWritten Exercises 202\u003c\/p\u003e \u003cp\u003eComputer Exercises 205\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Optimal Coordination of Inverse-Time DOCRs with Unified TCCC 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Mathematical Problem Formulation 207\u003c\/p\u003e \u003cp\u003e7.1.1 Objective Function 208\u003c\/p\u003e \u003cp\u003e7.1.1.1 Other Possible Objective Functions 210\u003c\/p\u003e \u003cp\u003e7.1.2 Inequality Constraints on Relay Operating Times 211\u003c\/p\u003e \u003cp\u003e7.1.3 Side Constraints on Relay Time Multiplier Settings 211\u003c\/p\u003e \u003cp\u003e7.1.4 Side Constraints on Relay Plug Settings 211\u003c\/p\u003e \u003cp\u003e7.1.5 Selectivity Constraint Among Primary and Backup Relay Pairs 212\u003c\/p\u003e \u003cp\u003e7.1.5.1 Transient Selectivity Constraint 213\u003c\/p\u003e \u003cp\u003e7.1.6 Standard Optimization Model 216\u003c\/p\u003e \u003cp\u003e7.2 Optimal Coordination of DOCRs Using Meta-Heuristic Optimization Algorithms 217\u003c\/p\u003e \u003cp\u003e7.2.1 Algorithm Implementation 217\u003c\/p\u003e \u003cp\u003e7.2.2 Constraint-Handling Techniques 218\u003c\/p\u003e \u003cp\u003e7.2.3 Solving the Infeasibility Condition 222\u003c\/p\u003e \u003cp\u003e7.3 Results Tester 228\u003c\/p\u003e \u003cp\u003eProblems 229\u003c\/p\u003e \u003cp\u003eWritten Exercises 229\u003c\/p\u003e \u003cp\u003eComputer Exercises 231\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Incorporating LP and Hybridizing It with Meta-heuristic Algorithms 235\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Model Linearization 235\u003c\/p\u003e \u003cp\u003e8.1.1 Classical Linearization Approach 236\u003c\/p\u003e \u003cp\u003e8.1.1.1 IEC Curves: Fixing Plug Settings and Varying Time Multiplier Settings 236\u003c\/p\u003e \u003cp\u003e8.1.1.2 IEEE Curves: Fixing Current Tap Settings and Varying Time Dial Settings 237\u003c\/p\u003e \u003cp\u003e8.1.2 Transformation-Based Linearization Approach 237\u003c\/p\u003e \u003cp\u003e8.1.2.1 IEC Curves: Fixing Time Multiplier Settings and Varying Plug Settings 238\u003c\/p\u003e \u003cp\u003e8.1.2.2 IEEE Curves: Fixing Time Dial Settings and Varying Current Tap Settings 238\u003c\/p\u003e \u003cp\u003e8.2 Multi-start Linear Programming 242\u003c\/p\u003e \u003cp\u003e8.3 Hybridizing Linear Programming with Population-Based Meta-heuristic Optimization Algorithms 245\u003c\/p\u003e \u003cp\u003e8.3.1 Classical Linearization Approach: Fixing PS\/CTS and Varying TMS\/TDS 245\u003c\/p\u003e \u003cp\u003e8.3.2 Transformation-Based Linearization Approach: Fixing TMS\/TDS and Varying Ps\/cts 245\u003c\/p\u003e \u003cp\u003e8.3.3 Innovative Linearization Approach: Fixing\/Varying TMS\/TDS and PS\/CTS 250\u003c\/p\u003e \u003cp\u003eProblems 250\u003c\/p\u003e \u003cp\u003eWritten Exercises 250\u003c\/p\u003e \u003cp\u003eComputer Exercises 251\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Optimal Coordination of DOCRs With OCRs and Fuses 253\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Simple Networks 253\u003c\/p\u003e \u003cp\u003e9.1.1 Protecting Radial Networks by Just OCRs 253\u003c\/p\u003e \u003cp\u003e9.1.2 Protecting Double-Line Networks by OCRs and DOCRs 255\u003c\/p\u003e \u003cp\u003e9.2 Little Harder Networks 257\u003c\/p\u003e \u003cp\u003e9.2.1 Combination of OCRs and DOCRs 258\u003c\/p\u003e \u003cp\u003e9.2.2 Combination of Fuses, OCRs, and DOCRs 261\u003c\/p\u003e \u003cp\u003e9.3 Complex Networks 264\u003c\/p\u003e \u003cp\u003eProblems 265\u003c\/p\u003e \u003cp\u003eWritten Exercises 265\u003c\/p\u003e \u003cp\u003eComputer Exercises 266\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Optimal Coordination with Considering Multiple Characteristic Curves 271\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 271\u003c\/p\u003e \u003cp\u003e10.2 Optimal Coordination of DOCRs with Multiple TCCCs 273\u003c\/p\u003e \u003cp\u003e10.3 Optimal Coordination of OCRs\/DOCRs with Multiple TCCCs 278\u003c\/p\u003e \u003cp\u003e10.4 Inherent Weaknesses of the Multi-TCCCs Approach 279\u003c\/p\u003e \u003cp\u003eProblems 280\u003c\/p\u003e \u003cp\u003eWritten Exercises 280\u003c\/p\u003e \u003cp\u003eComputer Exercises 281\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Optimal Coordination with Considering the Best TCCC 283\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 283\u003c\/p\u003e \u003cp\u003e11.2 Possible Structures of the Optimizer 284\u003c\/p\u003e \u003cp\u003e11.3 Technical Issue 287\u003c\/p\u003e \u003cp\u003eProblems 290\u003c\/p\u003e \u003cp\u003eWritten Exercises 290\u003c\/p\u003e \u003cp\u003eComputer Exercises 291\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Considering the Actual Settings of Different Relay Technologies in the Same Network 293\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 293\u003c\/p\u003e \u003cp\u003e12.2 Mathematical Formulation 294\u003c\/p\u003e \u003cp\u003e12.2.1 Objective Function 294\u003c\/p\u003e \u003cp\u003e12.2.2 Selectivity Constraint Among Primary and Backup Relay Pairs 295\u003c\/p\u003e \u003cp\u003e12.2.3 Inequality Constraints on Relay Operating Times 296\u003c\/p\u003e \u003cp\u003e12.2.4 Side Constraints on Relay Time Multiplier Settings 296\u003c\/p\u003e \u003cp\u003e12.2.5 Side Constraints on Relay Plug Settings 296\u003c\/p\u003e \u003cp\u003e12.3 Biogeography-Based Optimization Algorithm 297\u003c\/p\u003e \u003cp\u003e12.3.1 Clear Duplication Stage 297\u003c\/p\u003e \u003cp\u003e12.3.2 Avoiding Facing Infeasible Selectivity Constraints 297\u003c\/p\u003e \u003cp\u003e12.3.2.1 Linear Programming Stage 297\u003c\/p\u003e \u003cp\u003e12.3.3 Linking PS\u003ci\u003e\u003csub\u003e i\u003c\/sub\u003e\u003csup\u003e Yi\u003c\/sup\u003e\u003c\/i\u003eAnd TMS\u003csub\u003e i\u003c\/sub\u003e\u003ci\u003e\u003csup\u003eYi\u003c\/sup\u003e\u003c\/i\u003eWith \u003ci\u003eY\u003csub\u003ei \u003c\/sub\u003e\u003c\/i\u003e 298\u003c\/p\u003e \u003cp\u003e12.4 Further Discussion 299\u003c\/p\u003e \u003cp\u003eProblems 300\u003c\/p\u003e \u003cp\u003eWritten Exercises 300\u003c\/p\u003e \u003cp\u003eComputer Exercises 301\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Considering Double Primary Relay Strategy 303\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 303\u003c\/p\u003e \u003cp\u003e13.2 Mathematical Formulation 306\u003c\/p\u003e \u003cp\u003e13.2.1 Objective Function 307\u003c\/p\u003e \u003cp\u003e13.2.2 Selectivity Constraint 308\u003c\/p\u003e \u003cp\u003e13.2.3 Inequality Constraints on Relay Operating Times 308\u003c\/p\u003e \u003cp\u003e13.2.4 Side Constraints on Relay Time Multiplier Settings 308\u003c\/p\u003e \u003cp\u003e13.2.5 Side Constraints on Relay Plug Settings 309\u003c\/p\u003e \u003cp\u003e13.3 Possible Configurations of Double Primary ORC Problems 309\u003c\/p\u003e \u003cp\u003eProblems 315\u003c\/p\u003e \u003cp\u003eWritten Exercises 315\u003c\/p\u003e \u003cp\u003eComputer Exercises 316\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Adaptive ORC Solver 319\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 319\u003c\/p\u003e \u003cp\u003e14.2 Types of Network Changes 320\u003c\/p\u003e \u003cp\u003e14.2.1 Operational Changes 321\u003c\/p\u003e \u003cp\u003e14.2.2 Topological Changes 321\u003c\/p\u003e \u003cp\u003e14.3 AI-Based Adaptive ORC Solver 322\u003c\/p\u003e \u003cp\u003e14.3.1 Generating Datasets 323\u003c\/p\u003e \u003cp\u003e14.3.2 Applying ANN to Solve ORC Problems 324\u003c\/p\u003e \u003cp\u003eProblems 328\u003c\/p\u003e \u003cp\u003eWritten Exercises 328\u003c\/p\u003e \u003cp\u003eComputer Exercises 329\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Multi-objective Coordination 333\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Basic Principles 333\u003c\/p\u003e \u003cp\u003e15.1.1 Conventional Aggregation Method 334\u003c\/p\u003e \u003cp\u003e15.2 Multi-objective Formulation of ORC Problems 335\u003c\/p\u003e \u003cp\u003e15.2.1 Operating Time vs. System Reliability 336\u003c\/p\u003e \u003cp\u003e15.2.2 Operating Time vs. System Cost 336\u003c\/p\u003e \u003cp\u003e15.2.3 Operating Time vs. System Reliability vs. System Cost 342\u003c\/p\u003e \u003cp\u003e15.3 Further Discussions 342\u003c\/p\u003e \u003cp\u003eProblems 345\u003c\/p\u003e \u003cp\u003eWritten Exercises 345\u003c\/p\u003e \u003cp\u003eComputer Exercises 345\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Optimal Coordination of Distance and Overcurrent Relays 347\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 347\u003c\/p\u003e \u003cp\u003e16.2 Basic Mathematical Modeling 348\u003c\/p\u003e \u003cp\u003e16.3 Mathematical Modeling with Considering Multiple TCCCs 350\u003c\/p\u003e \u003cp\u003e16.3.1 Inequality Constraints 351\u003c\/p\u003e \u003cp\u003e16.3.2 Objective Function 352\u003c\/p\u003e \u003cp\u003e16.4 Mathematical Modeling with Considering Different Fault Locations 353\u003c\/p\u003e \u003cp\u003e16.4.1 Objective Function 353\u003c\/p\u003e \u003cp\u003e16.4.2 Inequality Constraints 354\u003c\/p\u003e \u003cp\u003e16.4.2.1 Near-End Faults 354\u003c\/p\u003e \u003cp\u003e16.4.2.2 Middle-Point Faults 354\u003c\/p\u003e \u003cp\u003e16.4.2.3 Far-End Faults 355\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Trending Topics and Existing Issues 357\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 New Inverse-Time Characteristics 357\u003c\/p\u003e \u003cp\u003e17.1.1 Scaled Standard TCCC Models 357\u003c\/p\u003e \u003cp\u003e17.1.2 Stepwise TCCCs 358\u003c\/p\u003e \u003cp\u003e17.1.3 New Customized TCCCs 359\u003c\/p\u003e \u003cp\u003e17.2 Smart Grid 359\u003c\/p\u003e \u003cp\u003e17.2.1 Distributed Generation 359\u003c\/p\u003e \u003cp\u003e17.2.2 Series Compensation and Flexible Alternating Current Transmission System 360\u003c\/p\u003e \u003cp\u003e17.2.3 Fault Current Limiters 360\u003c\/p\u003e \u003cp\u003e17.3 Economic Operation 360\u003c\/p\u003e \u003cp\u003e17.4 Power System Realization 361\u003c\/p\u003e \u003cp\u003e17.4.1 Power Lines 361\u003c\/p\u003e \u003cp\u003e17.4.2 Economic Operation 363\u003c\/p\u003e \u003cp\u003e17.4.2.1 Combined-Cycle Power Plants 364\u003c\/p\u003e \u003cp\u003e17.4.2.2 Degraded Efficiency Phenomenon 364\u003c\/p\u003e \u003cp\u003e17.4.2.3 Unaccounted Losses in Power Stations 365\u003c\/p\u003e \u003cp\u003e17.5 Locating Faults in Mesh Networks by DOCRs 367\u003c\/p\u003e \u003cp\u003e17.5.1 Mechanism of the Proposed Fault Location Algorithm 370\u003c\/p\u003e \u003cp\u003e17.5.1.1 Approach No. 1: Classical Linear Interpolation 373\u003c\/p\u003e \u003cp\u003e17.5.1.2 Approach No. 2: Logarithmic\/Nonlinear Interpolation 374\u003c\/p\u003e \u003cp\u003e17.5.1.3 Approach No. 3: Polynomial Regression 375\u003c\/p\u003e \u003cp\u003e17.5.1.4 Approach No. 4: Asymptotic Regression 375\u003c\/p\u003e \u003cp\u003e17.5.1.5 Approach No. 5: DTCC-Based Regression 375\u003c\/p\u003e \u003cp\u003e17.5.2 Final Structure of the Proposed Fault Locator 377\u003c\/p\u003e \u003cp\u003e17.5.3 Overall Accuracy vs. Uncertainty 379\u003c\/p\u003e \u003cp\u003e17.5.4 Further Discussion 380\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A Some Important Data Used in Power System Protection 381\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA. 1 Standard Current Transformer Ratios 381\u003c\/p\u003e \u003cp\u003eA. 2 Standard Device\/Function Number and Function Acronym Descriptions 382\u003c\/p\u003e \u003cp\u003eA.2. 1 Standard Device\/Function Numbers 382\u003c\/p\u003e \u003cp\u003eA.. 2 Device\/Function Acronyms 383\u003c\/p\u003e \u003cp\u003eA.2. 3 Suffix Letters 383\u003c\/p\u003e \u003cp\u003eA.2.3. 1 Auxiliary Devices 383\u003c\/p\u003e \u003cp\u003eA..3. 2 Actuating Quantities 383\u003c\/p\u003e \u003cp\u003eA.2.. 3 Main Device 384\u003c\/p\u003e \u003cp\u003eA.2.3. 4 Main Device Parts 384\u003c\/p\u003e \u003cp\u003eA.2.3. 5 Other Suffix Letters 384\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B How to Install PowerWorld Simulator (Education Version) 387\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix C Single-Machine Infinite Bus 391\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix D Linearizing Relay Operating Time Models 393\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eD.1 Linearizing the IEC\/BS Model of DOCRs by Fixing Time Multiplier Settings 393\u003c\/p\u003e \u003cp\u003eD.2 Linearizing the ANSI\/IEEE Model of DOCRs by Fixing Time Multiplier Settings 394\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix E Derivation of the First Order Thermal Differential Equation 397\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix F List of ORC Test Systems 399\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eF. 1 Three-Bus Test Systems 399\u003c\/p\u003e \u003cp\u003eF.. 1 System No. 1 399\u003c\/p\u003e \u003cp\u003eF.1. 2 System No. 2 399\u003c\/p\u003e \u003cp\u003eF. 2 Four-Bus Test Systems 403\u003c\/p\u003e \u003cp\u003eF.2. 1 System No. 1 403\u003c\/p\u003e \u003cp\u003eF.. 2 System No. 2 403\u003c\/p\u003e \u003cp\u003eF. 3 Five-Bus Test System 408\u003c\/p\u003e \u003cp\u003eF. 4 Six-Bus Test Systems 410\u003c\/p\u003e \u003cp\u003eF.4. 1 System No. 1 410\u003c\/p\u003e \u003cp\u003eF.4. 2 System No. 2 410\u003c\/p\u003e \u003cp\u003eF.4. 3 System No. 3 411\u003c\/p\u003e \u003cp\u003eF.. 4 System No. 4 413\u003c\/p\u003e \u003cp\u003eF. 5 Eight-Bus Test Systems 418\u003c\/p\u003e \u003cp\u003eF.5. 1 System No. 1 418\u003c\/p\u003e \u003cp\u003eF.5. 2 System No. 2 422\u003c\/p\u003e \u003cp\u003eF.5. 3 System No. 3 423\u003c\/p\u003e \u003cp\u003eF.5. 4 System No. 4 424\u003c\/p\u003e \u003cp\u003eF.. 5 System No. 5 425\u003c\/p\u003e \u003cp\u003eF. 6 Nine-Bus Test System 427\u003c\/p\u003e \u003cp\u003eF. 7 14-Bus Test Systems 430\u003c\/p\u003e \u003cp\u003eF.7. 1 System No. 1 431\u003c\/p\u003e \u003cp\u003eF.7. 2 System No. 2 433\u003c\/p\u003e \u003cp\u003eF. 8 15-Bus Test System 437\u003c\/p\u003e \u003cp\u003eF. 9 30-Bus Test Systems 441\u003c\/p\u003e \u003cp\u003eF.9. 1 System No. 1 441\u003c\/p\u003e \u003cp\u003eF.9. 2 System No. 2 444\u003c\/p\u003e \u003cp\u003eF. 10 42-Bus Test System 448\u003c\/p\u003e \u003cp\u003eF. 11 118-Bus Test System 453\u003c\/p\u003e \u003cp\u003eReferences 457\u003c\/p\u003e \u003cp\u003eIndex 479\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407155568983,"sku":"9781119794851","price":101.66,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119794851.jpg?v=1730498364","url":"https:\/\/bookcurl.com\/products\/optimal-coordination-of-power-protective-devices-with-illustrative-examples-9781119794851","provider":"Book Curl","version":"1.0","type":"link"}