Optimal Coordination of Power Protective Devices with Illustrative Examples

ISBN-13: 9781119794851 / Angielski / Twarda / 2021 / 528 str.

Ali Ridha

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Author Biography xviPreface xviiAcknowledgments xviiiAcronyms xixAbout The Companion Website xxiiiIntroduction xxv1 Fundamental Steps in Optimization Algorithms 11.1 Overview 11.1.1 Design Variables 41.1.2 Design Parameters 41.1.3 Design Function 51.1.4 Objective Function(s) 51.1.5 Design Constraints 71.1.5.1 Mathematical Constraints 81.1.5.2 Inequality Constraints 81.1.5.3 Side Constraints 91.1.6 General Principles 101.1.6.1 Feasible Space vs. Search Space 101.1.6.2 Global Optimum vs. Local Optimum 111.1.6.3 Types of Problem 121.1.7 Standard Format 121.1.8 Constraint-Handling Techniques 131.1.8.1 Random Search Method 171.1.8.2 Constant Penalty Function 171.1.8.3 Binary Static Penalty Function 181.1.8.4 Superiority of Feasible Points (SFPs) - Type I 181.1.8.5 Superiority of Feasible Points (SFP) - Type II 181.1.8.6 Eclectic Evolutionary Algorithm 181.1.8.7 Typical Dynamic Penalty Function 191.1.8.8 Exponential Dynamic Penalty Function 191.1.8.9 Adaptive Multiplication Penalty Function 191.1.8.10 Self-Adaptive Penalty Function (SAPF) 201.1.9 Performance Criteria Used to Evaluate Algorithms 211.1.10 Types of Optimization Techniques 231.2 Classical Optimization Algorithms 231.2.1 Linear Programming 251.2.1.1 Historical Time-Line 251.2.1.2 Mathematical Formulation of LP Problems 261.2.1.3 Linear Programming Solvers 261.2.2 Global-Local Optimization Strategy 281.2.2.1 Multi-Start Linear Programming 291.2.2.2 Hybridizing LP with Meta-Heuristic Optimization Algorithms as a Fine-Tuning Unit 311.3 Meta-Heuristic Algorithms 331.3.1 Biogeography-Based Optimization 341.3.1.1 Migration Stage 401.3.1.2 Mutation Stage 411.3.1.3 Clear Duplication Stage 431.3.1.4 Elitism Stage 441.3.1.5 The Overall BBO Algorithm 451.3.2 Differential Evolution 451.4 Hybrid Optimization Algorithms 461.4.1 BBO-LP 481.4.2 BBO/DE 51Problems 51Written Exercises 51Computer Exercises 532 Fundamentals of Power System Protection 572.1 Faults Classification 572.2 Protection System 612.3 Zones of Protection 652.4 Primary and Backup Protection 662.5 Performance and Design Criteria 662.5.1 Reliability 662.5.1.1 Dependability 662.5.1.2 Security 662.5.2 Sensitivity 672.5.3 Speed 672.5.4 Selectivity 672.5.5 Performance versus Economics 672.5.6 Adequateness 672.5.7 Simplicity 672.6 Overcurrent Protective Devices 672.6.1 Fuses 682.6.2 Bimetallic Relays 692.6.3 Overcurrent Protective Relays 692.6.4 Instantaneous OCR (IOCR) 702.6.5 Definite Time OCR (DTOCR) 712.6.6 Inverse Time OCR (ITOCR) 722.6.7 Mixed Characteristic Curves 732.6.7.1 Definite-Time Plus Instantaneous 732.6.7.2 Inverse-Time Plus Instantaneous 742.6.7.3 Inverse-Time Plus Definite-Time Plus Instantaneous 742.6.7.4 Inverse-Time Plus Definite-Time 752.6.7.5 Inverse Definite Minimum Time (IDMT) 76Problems 76Written Exercises 76Computer Exercises 773 Mathematical Modeling of Inverse-Time Overcurrent Relay Characteristics 793.1 Computer Representation of Inverse-Time Overcurrent Relay Characteristics 793.1.1 Direct Data Storage 793.1.2 Curve Fitting Formulas 823.1.2.1 Polynomial Equations 823.1.2.2 Exponential Equations 893.1.2.3 Artificial Intelligence 933.1.3 Special Models 943.1.3.1 RI-Type Characteristic 943.1.3.2 RD-Type Characteristic 953.1.3.3 FR Short Time Inverse 953.1.3.4 UK Rectifier Protection 953.1.3.5 BNP-Type Characteristic 953.1.3.6 Standard CO Series Characteristics 953.1.3.7 IAC and ANSI Special Equations 963.1.4 User-Defined Curves 983.2 Dealing with All the Standard Characteristic Curves Together 993.2.1 Differentiating Between Time Dial Setting and Time Multiplier Setting 993.2.2 Dealing with Time Dial Setting and Time Multiplier Setting as One Variable 1043.2.2.1 Fixed Divisor 1063.2.2.2 Linear Interpolation 1083.2.3 General Guidelines Before Conducting Researches and Studies 111Problems 113Written Exercises 113Computer Exercises 1144 Upper Limit of Relay Operating Time 1174.1 Do We Need to Define T¯max ? 1174.2 How to Define T¯max ? 1184.2.1 Thermal Equations 1184.2.1.1 Thermal Overload Protection for 3Phi Overhead Lines and Cables 1184.2.1.2 Thermal Overload Protection for Motors 1224.2.1.3 Thermal Overload Protection for Transformers 1244.2.2 Stability Analysis 126Problems 136Written Exercises 136Computer Exercises 1385 Directional Overcurrent Relays and the Importance of Relay Coordination 1395.1 Relay Grading in Radial Systems 1395.1.1 Time Grading 1405.1.2 Current Grading 1405.1.3 Inverse-Time Grading 1435.2 Directional Overcurrent Relays 1465.3 Coordination of DOCRs 1485.4 Is the Coordination of DOCRs an Iterative Problem? 1485.5 Minimum Break-Point Set 1615.6 Summary 163Problems 164Written Exercises 164Computer Exercises 1666 General Mechanism to Optimally Coordinate Directional Overcurrent Relays 1696.1 Constructing Power Network 1696.2 Power Flow Analysis 1706.2.1 Per-Unit System and Three-to-One-Phase Conversion 1726.2.2 Power Flow Solvers 1736.2.3 How to Apply the Newton-Raphson Method 1756.2.4 Sparsity Effect 1796.3 P/B Pairs Identification 1866.3.1 Inspection Method 1866.3.2 Graph Theory Methods 1866.3.3 Special Software 1886.4 Short-Circuit Analysis 1896.4.1 Short-Circuit Calculations 1896.4.2 Electric Power Engineering Software Tools 1906.4.2.1 Minimum Short-Circuit Current 1906.4.2.2 Maximum Short-Circuit Current 1926.4.3 Most Popular Standards 1936.4.3.1 ANSI/IEEE Standards C37 & UL 489 1936.4.3.2 IEC 61363 Standard 1946.4.3.3 IEC 60909 Standard 1946.5 Applying Optimization Techniques 201Problems 202Written Exercises 202Computer Exercises 2057 Optimal Coordination of Inverse-Time DOCRs with Unified TCCC 2077.1 Mathematical Problem Formulation 2077.1.1 Objective Function 2087.1.1.1 Other Possible Objective Functions 2107.1.2 Inequality Constraints on Relay Operating Times 2117.1.3 Side Constraints on Relay Time Multiplier Settings 2117.1.4 Side Constraints on Relay Plug Settings 2117.1.5 Selectivity Constraint Among Primary and Backup Relay Pairs 2127.1.5.1 Transient Selectivity Constraint 2137.1.6 Standard Optimization Model 2167.2 Optimal Coordination of DOCRs Using Meta-Heuristic Optimization Algorithms 2177.2.1 Algorithm Implementation 2177.2.2 Constraint-Handling Techniques 2187.2.3 Solving the Infeasibility Condition 2227.3 Results Tester 228Problems 229Written Exercises 229Computer Exercises 2318 Incorporating LP and Hybridizing It with Meta-heuristic Algorithms 2358.1 Model Linearization 2358.1.1 Classical Linearization Approach 2368.1.1.1 IEC Curves: Fixing Plug Settings and Varying Time Multiplier Settings 2368.1.1.2 IEEE Curves: Fixing Current Tap Settings and Varying Time Dial Settings 2378.1.2 Transformation-Based Linearization Approach 2378.1.2.1 IEC Curves: Fixing Time Multiplier Settings and Varying Plug Settings 2388.1.2.2 IEEE Curves: Fixing Time Dial Settings and Varying Current Tap Settings 2388.2 Multi-start Linear Programming 2428.3 Hybridizing Linear Programming with Population-Based Meta-heuristic Optimization Algorithms 2458.3.1 Classical Linearization Approach: Fixing PS/CTS and Varying TMS/TDS 2458.3.2 Transformation-Based Linearization Approach: Fixing TMS/TDS and Varying PS/CTS 2458.3.3 Innovative Linearization Approach: Fixing/Varying TMS/TDS and PS/CTS 250Problems 250Written Exercises 250Computer Exercises 2519 Optimal Coordination of DOCRs With OCRs and Fuses 2539.1 Simple Networks 2539.1.1 Protecting Radial Networks by Just OCRs 2539.1.2 Protecting Double-Line Networks by OCRs and DOCRs 2559.2 Little Harder Networks 2579.2.1 Combination of OCRs and DOCRs 2589.2.2 Combination of Fuses, OCRs, and DOCRs 2619.3 Complex Networks 264Problems 265Written Exercises 265Computer Exercises 26610 Optimal Coordination with Considering Multiple Characteristic Curves 27110.1 Introduction 27110.2 Optimal Coordination of DOCRs with Multiple TCCCs 27310.3 Optimal Coordination of OCRs/DOCRs with Multiple TCCCs 27810.4 Inherent Weaknesses of the Multi-TCCCs Approach 279Problems 280Written Exercises 280Computer Exercises 28111 Optimal Coordination with Considering the Best TCCC 28311.1 Introduction 28311.2 Possible Structures of the Optimizer 28411.3 Technical Issue 287Problems 290Written Exercises 290Computer Exercises 29112 Considering the Actual Settings of Different Relay Technologies in the Same Network 29312.1 Introduction 29312.2 Mathematical Formulation 29412.2.1 Objective Function 29412.2.2 Selectivity Constraint Among Primary and Backup Relay Pairs 29512.2.3 Inequality Constraints on Relay Operating Times 29612.2.4 Side Constraints on Relay Time Multiplier Settings 29612.2.5 Side Constraints on Relay Plug Settings 29612.3 Biogeography-Based Optimization Algorithm 29712.3.1 Clear Duplication Stage 29712.3.2 Avoiding Facing Infeasible Selectivity Constraints 29712.3.2.1 Linear Programming Stage 29712.3.3 Linking PS¯yi ¯i and TMS¯yi ¯i with yi 29812.4 Further Discussion 299Problems 300Written Exercises 300Computer Exercises 30113 Considering Double Primary Relay Strategy 30313.1 Introduction 30313.2 Mathematical Formulation 30613.2.1 Objective Function 30713.2.2 Selectivity Constraint 30813.2.3 Inequality Constraints on Relay Operating Times 30813.2.4 Side Constraints on Relay Time Multiplier Settings 30813.2.5 Side Constraints on Relay Plug Settings 30913.3 Possible Configurations of Double Primary ORC Problems 309Problems 315Written Exercises 315Computer Exercises 31614 Adaptive ORC Solver 31914.1 Introduction 31914.2 Types of Network Changes 32014.2.1 Operational Changes 32114.2.2 Topological Changes 32114.3 AI-Based Adaptive ORC Solver 32214.3.1 Generating Datasets 32314.3.2 Applying ANN to Solve ORC Problems 324Problems 328Written Exercises 328Computer Exercises 32915 Multi-objective Coordination 33315.1 Basic Principles 33315.1.1 Conventional Aggregation Method 33415.2 Multi-objective Formulation of ORC Problems 33515.2.1 Operating Time vs. System Reliability 33615.2.2 Operating Time vs. System Cost 33615.2.3 Operating Time vs. System Reliability vs. System Cost 34215.3 Further Discussions 342Problems 345Written Exercises 345Computer Exercises 34516 Optimal Coordination of Distance and Overcurrent Relays 34716.1 Introduction 34716.2 Basic Mathematical Modeling 34816.3 Mathematical Modeling with Considering Multiple TCCCs 35016.3.1 Inequality Constraints 35116.3.2 Objective Function 35216.4 Mathematical Modeling with Considering Different Fault Locations 35316.4.1 Objective Function 35316.4.2 Inequality Constraints 35416.4.2.1 Near-End Faults 35416.4.2.2 Middle-Point Faults 35416.4.2.3 Far-End Faults 35517 Trending Topics and Existing Issues 35717.1 New Inverse-Time Characteristics 35717.1.1 Scaled Standard TCCC Models 35717.1.2 Stepwise TCCCs 35817.1.3 New Customized TCCCs 35917.2 Smart Grid 35917.2.1 Distributed Generation 35917.2.2 Series Compensation and Flexible Alternating Current Transmission System 36017.2.3 Fault Current Limiters 36017.3 Economic Operation 36017.4 Power System Realization 36117.4.1 Power Lines 36117.4.2 Economic Operation 36317.4.2.1 Combined-Cycle Power Plants 36417.4.2.2 Degraded Efficiency Phenomenon 36417.4.2.3 Unaccounted Losses in Power Stations 36517.5 Locating Faults in Mesh Networks by DOCRs 36717.5.1 Mechanism of the Proposed Fault Location Algorithm 37017.5.1.1 Approach No. 1: Classical Linear Interpolation 37317.5.1.2 Approach No. 2: Logarithmic/Nonlinear Interpolation 37417.5.1.3 Approach No. 3: Polynomial Regression 37517.5.1.4 Approach No. 4: Asymptotic Regression 37517.5.1.5 Approach No. 5: DTCC-Based Regression 37517.5.2 Final Structure of the Proposed Fault Locator 37717.5.3 Overall Accuracy vs. Uncertainty 37917.5.4 Further Discussion 380Appendix A Some Important Data Used in Power System Protection 381A.1 Standard Current Transformer Ratios 381A.2 Standard Device/Function Number and Function Acronym Descriptions 382A.2.1 Standard Device/Function Numbers 382A.2.2 Device/Function Acronyms 383A.2.3 Suffix Letters 383A.2.3.1 Auxiliary Devices 383A.2.3.2 Actuating Quantities 383A.2.3.3 Main Device 384A.2.3.4 Main Device Parts 384A.2.3.5 Other Suffix Letters 384Appendix B How to Install PowerWorld Simulator (Education Version) 387Appendix C Single-Machine Infinite Bus 391Appendix D Linearizing Relay Operating Time Models 393D.1 Linearizing the IEC/BS Model of DOCRs by Fixing Time Multiplier Settings 393D.2 Linearizing the ANSI/IEEE Model of DOCRs by Fixing Time Multiplier Settings 394Appendix E Derivation of the First Order Thermal Differential Equation 397Appendix F List of ORC Test Systems 399F.1 Three-Bus Test Systems 399F.1.1 System No. 1 399F.1.2 System No. 2 399F.2 Four-Bus Test Systems 403F.2.1 System No. 1 403F.2.2 System No. 2 403F.3 Five-Bus Test System 408F.4 Six-Bus Test Systems 410F.4.1 System No. 1 410F.4.2 System No. 2 410F.4.3 System No. 3 411F.4.4 System No. 4 413F.5 Eight-Bus Test Systems 418F.5.1 System No. 1 418F.5.2 System No. 2 422F.5.3 System No. 3 423F.5.4 System No. 4 424F.5.5 System No. 5 425F.6 Nine-Bus Test System 427F.7 14-Bus Test Systems 430F.7.1 System No. 1 431F.7.2 System No. 2 433F.8 15-Bus Test System 437F.9 30-Bus Test Systems 441F.9.1 System No. 1 441F.9.2 System No. 2 444F.10 42-Bus Test System 448F.11 118-Bus Test System 453References 457Index 479

O autorze

ALI R. AL-ROOMI, PhD, is a Research Assistant at Dalhousie University, Halifax, Canada. He is an IEEE Member and has served as an academic reviewer for Transactions on Automation Science and Engineering and Electrical Power and Energy Conference. His research interests include power systems operation, control systems, sensors, optimization algorithms, and machine learning computing systems.