Modern Music-Inspired Optimization Algorithms for Electric Power Systems (eBook)

Foreword 7
Preface 9
Acknowledgments 17
Contents 18
About the Authors 25
Part I: Fundamental Concepts of Optimization Problems and Theory of Meta-Heuristic Music-Inspired Optimization Algorithms 27
Chapter 1: Introduction to Meta-heuristic Optimization Algorithms 28
1.1 Introduction 28
1.2 An Optimization Problem and Its Parameters 29
1.2.1 Mathematical Description of an Optimization Problem 29
1.3 Classification of an Optimization Problem 31
1.3.1 Classification of Optimization Problems from the Perspective of a Number of Objective Functions 31
1.3.2 Classification of Optimization Problems from the Perspective of Constraints 32
1.3.3 Classification of Optimization Problems from the Perspective of the Nature of Employed Equations 33
1.3.4 Classification of Optimization Problems from the Perspective of an Objective Functions Landscape 34
1.3.5 Classification of Optimization Problems from the Perspective of the Kind of Decision-Making Variables 34
1.3.6 Classification of Optimization Problems from the Perspective of the Number of Decision-Making Variables 35
1.3.7 Classification of Optimization Problems from the Perspective of the Separability of the Employed Equations 36
1.3.8 Classification of Optimization Problems from the Perspective of Uncertainty 36
1.4 Optimization Algorithms and Their Characteristics 37
1.5 Meta-heuristic Optimization Algorithms 38
1.5.1 Classification of Meta-heuristic Optimization Algorithms with a Focus on Inspirational Sources 39
1.5.1.1 Swarm Intelligence-Based Meta-heuristic Optimization Algorithms 39
1.5.1.2 Biologically Inspired Meta-heuristic Optimization Algorithms Not Based on Swarm Intelligence 40
1.5.1.3 Physics- and Chemistry-Based Meta-heuristic Optimization Algorithms 40
1.5.1.4 Human Behavior- and Society-Inspired Meta-heuristic Optimization Algorithms 41
1.5.1.5 Some Hints Concerning the Architecture of Meta-heuristic Optimization Algorithms 41
1.6 Conclusions 42
Appendix 1: List of Abbreviations and Acronyms 42
Appendix 2: List of Mathematical Symbols 43
References 44
Chapter 2: Introduction to Multi-objective Optimization and Decision-Making Analysis 46
2.1 Introduction 46
2.2 Necessity of Using Multi-objective Optimization 48
2.3 Fundamental Concepts of Optimization in the MOOPs 49
2.3.1 Mathematical Description of a MOOP 49
2.3.2 Concepts Associated with Efficiency, Efficient frontier, and Dominance 50
2.3.3 Concepts Pertaining to Pareto Optimality 51
2.3.4 Concepts Related to the Vector of Ideal Objective Functions and the Vector of Nadir Objective Functions 53
2.3.5 Concepts Relevant to the Investigation of Pareto Optimality 55
2.4 Multi-objective Optimization Algorithms 55
2.4.1 Noninteractive Approaches 56
2.4.1.1 Basic Approaches 56
2.4.1.2 No-Preference Approaches 60
2.4.1.3 A Priori Approaches 60
2.4.1.4 A Posteriori Approaches 61
2.4.2 Interactive Approaches 61
2.5 Selection of the Final Solution by Using a Fuzzy Satisfying Method 63
2.5.1 Conservative Methodology 65
2.5.2 Distance Metric Methodology 66
2.5.3 Step-by-Step Process for Implementing the FSM 66
2.6 Conclusions 67
Appendix 1: List of Abbreviations and Acronyms 68
Appendix 2: List of Mathematical Symbols 68
References 70
Chapter 3: Music-Inspired Optimization Algorithms: From Past to Present 71
3.1 Introduction 71
3.2 A Brief Review of Music 74
3.2.1 The Definition of Music 74
3.2.2 A Brief Review of Music History 75
3.2.3 The Interdependencies of Phenomena and Concepts of Music and the Optimization Problem 75
3.3 Harmony Search Algorithm 77
3.3.1 Stage 1: Definition Stage-Definition of the Optimization Problem and its Parameters 78
3.3.2 Stage 2: Initialization Stage 79
3.3.2.1 Sub-stage 2.1: Initialization of the Parameters of the SS-HSA 79
3.3.2.2 Sub-stage 2.2: Initialization of the HM 80
3.3.3 Stage 3: Computational Stage 81
3.3.3.1 Sub-stage 3.1: Improvisation of a New Harmony Vector 83
3.3.3.2 Sub-stage 3.2: Update of the HM 85
3.3.3.3 Sub-stage 3.3: Check of the Stopping Criterion of the SS-HSA 87
3.3.4 Stage 4: Selection Stage-Selection of the Final Optimal Solution-The Best Harmony 87
3.4 Enhanced Versions of the Single-Stage Computational, Single-Dimensional Harmony Search Algorithm 89
3.5 Improved Harmony Search Algorithm 90
3.6 Melody Search Algorithm 93
3.6.1 Stage 1: Definition Stage-Definition of the Optimization Problem and its Parameters 97
3.6.2 Stage 2: Initialization Stage 98
3.6.2.1 Sub-stage 2.1: Initialization of the Parameters of the TMS-MSA 98
3.6.2.2 Sub-stage 2.2: Initialization of the MM 100
3.6.3 Stage 3: Single Computational Stage or SIS 103
3.6.3.1 Sub-stage 3.1: Improvisation of a New Melody Vector by Each Player 103
3.6.3.2 Sub-stage 3.2: Update of Each PM 104
3.6.3.3 Sub-stage 3.3: Check of the Stopping Criterion of the SIS 105
3.6.4 Stage 4: Pseudo-Group Computational Stage or PGIS 106
3.6.4.1 Sub-stage 4.1: Improvisation of a New Melody Vector by Each Player Taking into Account the Feasible Ranges of the Upda... 106
3.6.4.2 Sub-stage 4.2: Update of Each PM 106
3.6.4.3 Sub-stage 4.3: Update of the Feasible Ranges of Pitches-Continuous Decision-Making Variables-for the Next Improvisatio... 106
3.6.4.4 Sub-stage 4.4: Check of the Stopping Criterion of the PGIS 107
3.6.5 Stage 5: Selection Stage-Selection of the Final Optimal Solution-The Best Melody 108
3.6.6 Alternative Improvisation Procedure 109
3.7 Conclusions 115
Appendix 1: List of Abbreviations and Acronyms 115
Appendix 2: List of Mathematical Symbols 116
References 119
Chapter 4: Advances in Music-Inspired Optimization Algorithms 120
4.1 Introduction 120
4.2 Continuous/Discrete TMS-MSA 123
4.2.1 Stage 1: Definition Stage-Definition of the Optimization Problem and Its Parameters 124
4.2.2 Stage 2: Initialization Stage 125
4.2.2.1 Sub-stage 2.1: Initialization of the Parameters of the Proposed Continuous/Discrete TMS-MSA 125
4.2.2.2 Sub-stage 2.2: Initialization of the MM 125
4.2.3 Stage 3: Single Computational Stage or SIS 127
4.2.3.1 Sub-stage 3.1: Improvisation of a New Melody Vector by Each Player 127
4.2.3.2 Sub-stage 3.2: Update of Each PM 129
4.2.3.3 Sub-stage 3.3: Check of the Stopping Criterion of the SIS 130
4.2.4 Stage 4: Pseudo-Group Computational Stage or PGIS 130
4.2.4.1 Sub-stage 4.1: Improvisation of a New Melody Vector by Each Player 131
4.2.4.2 Sub-stage 4.2: Update of Memory of Each Player 132
4.2.4.3 Sub-stage 4.3: Update of the Feasible Ranges of Pitches-Continuous Decision-Making Variables for the Next Improvisatio... 132
4.2.4.4 Sub-stage 4.4: Check of the Stopping Criterion of the Pseudo-Group Improvisation Stage 132
4.2.5 Stage 5: Selection Stage-Selection of the Final Optimal Solution-The Most Favorable Melody 132
4.2.6 Continuous/Discrete Alternative Improvisation Procedure 134
4.3 Enhanced Version of the Proposed Continuous/Discrete TMS-MSA 139
4.4 Multi-stage Computational Multi-dimensional Multiple-Homogeneous Enhanced Melody Search Algorithm: Symphony Orchestra Sear... 157
4.4.1 Stage 1: Definition Stage-Definition of the Optimization Problem and Its Parameters 165
4.4.2 Stage 2: Initialization Stage 166
4.4.2.1 Sub-stage 2.1: Initialization of the Parameters of the SOSA 166
4.4.2.2 Sub-stage 2.2: Initialization of the Symphony Orchestra Memory 169
4.4.3 Stage 3: Single Computational Stage or SIS 171
4.4.3.1 Sub-stage 3.1: Improvisation of a New Melody Vector by Each Player in the Symphony Orchestra 171
4.4.3.2 Sub-stage 3.2: Update of Each Available PM in the Symphony Orchestra 173
4.4.3.3 Sub-stage 3.3: Check of the Stopping Criterion of the SIS 174
4.4.4 Stage 4: Group Computational Stage for Each Homogeneous Musical Group or GISHMG 174
4.4.4.1 Sub-stage 4.1: Improvisation of a New Melody Vector by Each Player in the Symphony Orchestra Taking into Account the F... 175
4.4.4.2 Sub-stage 4.2: Update of Each Available PM in the Symphony Orchestra 177
4.4.4.3 Sub-stage 4.3: Update of the Feasible Ranges of the Pitches-Continuous Decision-Making Variables-for Each Homogeneous ... 177
4.4.4.4 Sub-stage 4.4: Check of the Stopping Criterion of the GISHMG 177
4.4.5 Stage 5: Group Computational Stage for the Inhomogeneous Musical Ensemble or GISIME 178
4.4.5.1 Sub-stage 5.1: Improvisation of a New Melody Vector by Each Player in the Symphony Orchestra Taking into Account the F... 179
4.4.5.2 Sub-stage 5.2: Update of Each Available PM in the Symphony Orchestra 180
4.4.5.3 Sub-stage 5.3: Update of the Feasible Ranges of the Pitches-Continuous Decision-Making Variables-for the Inhomogeneous... 180
4.4.5.4 Sub-stage 5.4: Check of the Stopping Criterion of the GISIME 180
4.4.6 Stage 6: Selection Stage-Selection of the Final Optimal Solution-the Best Melody 182
4.4.7 Novel Improvisation Procedure 183
4.4.8 Some Hints Regarding the Architecture of the Proposed SOSA 190
4.5 Multi-objective Strategies for the Music-Inspired Optimization Algorithms 196
4.5.1 Multi-objective Strategies for the Meta-heuristic Music-Inspired Optimization Algorithms with Single-Stage Computational... 196
4.5.1.1 Multi-objective Strategy for the SS-HSA 197
4.5.1.2 Multi-objective Strategy for the SS-IHSA 212
4.5.2 Multi-objective Strategies for the Meta-heuristic Music-Inspired Optimization Algorithms with Two-Stage Computational Mu... 215
4.5.2.1 Multi-objective Strategy for the Proposed Continuous/Discrete TMS-MSA 215
4.5.2.2 Multi-objective Strategy for the Proposed TMS-EMSA 235
4.5.3 Multi-objective Strategy for the Meta-heuristic Music-Inspired Optimization Algorithms with Multi-stage Computational Mu... 245
4.6 Conclusions 271
Appendix 1: List of Abbreviations and Acronyms 276
Appendix 2: List of Mathematical Symbols 278
References 285
Part II: Power Systems Operation and Planning Problems 286
Chapter 5: Power Systems Operation 287
5.1 Introduction 287
5.2 A Brief Review of Game Theory 289
5.2.1 Classifications of the Game 289
5.2.2 The Concept of Nash Equilibrium 291
5.2.3 Modeling of Game Theory in the Electricity Markets with Imperfect Competition 292
5.2.3.1 Cournot-Based Model and/or Playing with Quantities 292
5.2.3.2 Stackelberg Leadership-Based Model 294
5.2.3.3 Bertrand-Based Model and Playing with Prices 294
5.2.3.4 The Supply Function Equilibrium-Based Model 295
5.3 A Bilateral Bidding Mechanism in the Competitive Security-Constrained Electricity Market: A Bi-Level Computational-Logical... 298
5.3.1 Bilateral Bidding Strategy Model: First Level (Problem A) 299
5.3.1.1 Mathematical Model of Bidding Strategies for GENCOs 302
5.3.1.2 Mathematical Model of a Bidding Strategy for DISCOs 305
5.3.2 Security-Constrained Electricity Market Model: Second Level (Problem B) 308
5.3.3 Overview of the Bi-Level Computational-Logical Framework 312
5.3.4 Solution Method and Implementation Considerations 314
5.3.5 Simulation Results and Case Studies 315
5.3.5.1 First Case: Simulation Results and Discussion 318
5.3.5.2 Second Case: Simulation Results and Discussion 321
5.3.5.3 Performance Evaluation of the Proposed Music-Inspired Optimization Algorithms 331
5.4 Conclusions 335
Appendix 1: List of Abbreviations and Acronyms 337
Appendix 2: List of Mathematical Symbols 338
Appendix 3: Input data 340
References 346
Chapter 6: Power Systems Planning 348
6.1 Introduction 348
6.2 A Brief Review of Power System Planning Studies 350
6.2.1 Why Do the Power Systems Need the Expansion Planning? 350
6.2.2 A Brief Review of Power System Planning Structure 350
6.2.3 Power System Planning Issues 351
6.2.3.1 From the Standpoint of Power System Structure 352
6.2.3.2 From the Standpoint of the Planning Horizon 353
6.2.3.3 From the Standpoint of the Uncertainties 354
6.2.3.4 From the Standpoint of the Solving Algorithms 357
6.3 Pseudo-Dynamic Generation Expansion Planning: A Strategic Tri-level Computational-Logical Framework 358
6.3.1 Mathematical Model of the Deterministic Strategic Tri-level Computational-Logical Framework 359
6.3.1.1 Bilateral Bidding Mechanism: First Level (Problem A) 362
6.3.1.2 Competitive Security-Constrained Electricity Market: Second Level (Problem B) 362
6.3.1.3 Pseudo-Dynamic Generation Expansion Planning: Third Level (Problem C) 363
6.3.2 Overview of the Deterministic Strategic Tri-level Computational-Logical Framework 368
6.3.3 Mathematical Model of the Risk-Driven Strategic Tri-level Computational-Logical Framework 372
6.3.3.1 The IGDT Severe Twofold Uncertainty Model 373
6.3.3.2 The IGDT Risk-Averse Decision-Making Policy: Robustness Function 376
6.3.3.3 The IGDT Risk-Taker Decision-Making Strategy: Opportunity Function 379
6.3.4 Solution Method and Implementation Considerations 382
6.3.5 Simulation Results and Case Studies 383
6.3.5.1 First Case: Simulation Results and Discussion 387
6.3.5.2 Second Case: Simulation Results and Discussion 399
6.3.5.3 Quantitative Verification of the Proposed IGDT Risk-Taker Decision-Making Policy in Comparison to a Robust Optimizatio... 413
6.3.5.4 Performance Evaluation of the Proposed Optimization Algorithms: Simulation Results and Discussion 413
6.4 Pseudo-Dynamic Transmission Expansion Planning: A Strategic Tri-level Computational-Logical Framework 423
6.4.1 Mathematical Model of the Deterministic Strategic Tri-level Computational-Logical Framework 426
6.4.1.1 Bilateral Bidding Mechanism: First Level (Problem A) 426
6.4.1.2 Competitive Security-Constrained Electricity Market: Second Level (Problem B) 426
6.4.1.3 Pseudo-Dynamic Transmission Expansion Planning: Third Level (Problem C) 426
6.4.2 Overview of the Deterministic Strategic Tri-level Computational-Logical Framework 431
6.4.3 Mathematical Model of the Risk-Driven Strategic Tri-level Computational-Logical Framework 434
6.4.3.1 The IGDT Severe Twofold Uncertainty Model 435
6.4.3.2 The IGDT Risk-Averse Decision-Making Policy: Robustness Function 435
6.4.3.3 The IGDT Risk-Taker Decision-Making Policy: Opportunity Function 438
6.4.4 Solution Method and Implementation Considerations 440
6.4.5 Simulation Results and Case Studies 441
6.4.5.1 The Modified IEEE 30-Bus Test System 443
6.4.5.1.1 First Case: Simulation Results and Discussion 446
6.4.5.1.2 Second Case: Simulation Results and Discussion 456
6.4.5.2 Large-Scale Iranian 400 kV Transmission Network 463
6.4.5.2.1 First Case: Simulation Results and Discussion 471
6.4.5.2.2 Second Case: Simulation Results and Discussion 471
6.4.5.2.3 Investigation of the Effects of Volatility in Market Price and Demand Uncertainties 473
6.4.5.2.4 Quantitative Verification of the Proposed IGDT Risk-Averse Decision-Making Policy in Comparison to the Robust Optimi... 478
6.4.5.2.5 Performance Evaluation of the Proposed Optimization Algorithms: Simulation Results and Discussion 481
6.5 Coordination of Pseudo-Dynamic Generation and Transmission Expansion Planning: A Strategic Quad-Level Computational-Logica... 487
6.5.1 Mathematical Model of the Deterministic Strategic Quad-Level Computational-Logical Framework 488
6.5.1.1 Bilateral Bidding Mechanism: First Level (Problem A) 488
6.5.1.2 Competitive Security-Constrained Electricity Market: Second Level (Problem B) 491
6.5.1.3 Pseudo-Dynamic Generation Expansion Planning: Third Level (Problem C) 492
6.5.1.4 Pseudo-Dynamic Transmission Expansion Planning: Fourth Level (Problem D) 492
6.5.2 Overview of the Deterministic Strategic Quad-Level Computational-Logical Framework 492
6.5.3 Mathematical Model of the Risk-Driven Strategic Quad-Level Computational-Logical Framework 500
6.5.3.1 The IGDT Severe Twofold Uncertainty Model 500
6.5.3.2 The IGDT Risk-Averse Decision-Making Policy: Robustness Function 500
6.5.3.3 The IGDT Risk-Taker Decision-Making Policy: Opportunity Function 503
6.5.4 Solution Method and Implementation Considerations 506
6.5.5 Simulation Results and Case Studies 509
6.5.5.1 First Case: Simulation Results and Discussion 514
6.5.5.2 Second Case: Simulation Results and Discussion 517
6.5.5.3 Investigation into the Performance of the Proposed Framework Under the Coordinated and Uncoordinated Decisions for the... 520
6.5.5.4 Quantitative Verification of the Proposed IGDT Risk-Averse Decision-Making Policy in Comparison to the Robust Optimiza... 524
6.5.5.5 Performance Evaluation of the Proposed Optimization Algorithms: Simulation Results and Discussion 527
6.6 Pseudo-Dynamic Open-Loop Distribution Expansion Planning: A Techno-Economic Framework 540
6.6.1 Mathematical Model of the Deterministic Techno-Economic Framework 541
6.6.2 Mathematical Model of the Risk-Driven Techno-Economic Framework 553
6.6.2.1 The IGDT Severe Twofold Uncertainty Model 553
6.6.2.2 The IGDT Risk-Averse Decision-Making Model: Robustness Function 555
6.6.2.3 The IGDT Risk-Taker Decision-Making Model: Opportunity Function 556
6.6.3 Solution Method and Implementation Considerations 558
6.6.4 Simulation Results and Case Studies 559
6.6.4.1 First Case: Simulation Results and Discussion 563
6.6.4.2 Second Case: Simulation Results and Discussion 569
6.6.4.3 The Impact of the Presence of Distributed Generation Resources on the Voltage Profile 574
6.6.4.4 Quantitative Verification of the Proposed IGDT Risk-Averse Decision-Making Policy in Comparison to the Robust Optimiza... 576
6.6.4.5 Performance Evaluation of the Proposed Optimization Algorithms: Simulation Results and Discussion 578
6.7 Conclusions 589
Appendix 1: List of Abbreviations and Acronyms 592
Appendix 2: List of Mathematical Symbols 594
Appendix 3: Input Data 607
References 642
Chapter 7: Power Filters Planning 647
7.1 Introduction 647
7.2 A Brief Review of Harmonic Power Filter Planning Studies 649
7.2.1 Nonlinear Loads and Their Malicious Effects 650
7.2.2 Harmonic Power Filters 651
7.2.3 Harmonic Power Flow 653
7.2.4 Harmonic Power Filter Planning Problem 654
7.3 Hybrid Harmonic Power Filter Planning: A Techno-economic Framework 655
7.3.1 Mathematical Model of the Techno-economic Multi-objective Framework 656
7.3.1.1 Deterministic Decoupled Harmonic Power Flow Methodology 659
7.3.1.2 Passive and Active Harmonic Power Filters 666
7.3.1.3 Hybrid Harmonic Power Filter Planning Problem 670
7.3.1.4 Probabilistic Decoupled Harmonic Power Flow Methodology 677
7.3.2 Solution Method and Implementation Considerations 681
7.3.3 Simulation Results and Case Studies 681
7.3.3.1 IEEE 18-Bus Distorted Test Network 682
7.3.3.1.1 First Case: Simulation Results and Discussion 687
7.3.3.1.2 Second Case: Simulation Results and Discussion 692
7.3.3.1.3 Third Case: Simulation Results and Discussion 695
7.3.3.1.4 Investigation of Passive Harmonic Power Filter Performance 700
7.3.3.2 The 34-Bus Distribution Test Network 701
7.3.3.2.1 First Case: Simulation Results and Discussion 704
7.3.3.2.2 Second Case: Simulation Results and Discussion 705
7.3.3.2.3 Third Case: Simulation Results and Discussion 706
7.3.3.2.4 Performance Evaluation of the Proposed Optimization Algorithms: Simulation Results and Discussion 709
7.4 Conclusions 717
Appendix 1: List of Abbreviations and Acronyms 720
Appendix 2: List of Mathematical Symbols 721
Appendix 3: Input Data 727
References 735
Index 737