2007. , 572 pages. The same problems considered, but different
methodology approach in comparison with soviet/russian electric
power school (Venikov, Sovalov, Gostein, Filippova, Obrezkov,
Malinin etc. ).
Preface
In response to increasing public awareness of the environmental situation and the plea for clean air, many engineers came up with new methods to reduce air pollution in parallel with pursuit of economy. Engineers are devoting considerable time to handle such conflicting situations through multiobjective optimization. The aim of multiobjective optimization is to help engineers (or decision makers) take the right decision in conflicting situations bedevilled with several objectives to be satisfied simultaneously. Further for large-scale integrated electric power systems, there is no other alteative but to use the digital computer as a computation tool for fast, accurate, and robust solution procedures.
This book is intended to serve as an introductory text to the topic of multiobjective optimization in electric power systems. It may also be used for self-study by practising personnel involved in planning and operation of thermal as well as integrated hydrothermal electric power systems. It has been the endeavour of the authors to provide simple and understandable basic computational algorithms so that students or practising engineers can develop their own programs in any high level language or improve the existing ones. Solved examples are given for better understanding of each power system problem discussed. The reader is expected to have a prior knowledge of basics of electric power system, optimization techniques, numerical methods, and matrix operations. The first chapter introduces the power system components, planning and operation problems, potential application of fuzzy theory and artificial neural networks in power systems.
Chapter 2 elaborates on power network modelling and important techniques of ac load flow analysis like Gauss-Seidel, Newton-Raphson, and decoupled load flow. To reduce the computation burden, initial guess for load flow is also explained. This chapter also deals with modelling and solution procedure for ac-dc load flow.
Chapter 3 is devoted to economic dispatch of thermal power systems. Newton-Raphson and approximations to Newton-Raphson method are discussed to solve the classical economic dispatch. The economic dispatch procedures are elaborated here to consider exact loss formula as well as real and reactive power balance. Rigorous economic dispatch techniques such as penalty factor method, gradient method, and Newton-Raphson method are discussed. The chapter also deals with the evaluation of Б-coefficients by classical method, F-bus method, and sensitivity factor method. It also explains the development of exact transmission loss formula.
Chapter 4 deals with the foundations of hydrothermal scheduling such as fixed-head, variable-head for short-term and long-term problems. It elaborates upon the classical Newton-Raphson and approximate Newton-Raphson methods to solve the fixed-head, short-range hydrothermal problem. Classical and approximate Newton-Raphson methods for short-range, variable-head, hydrothermal problems are also discussed in this chapter. It also deals with hydro plant modelling for long-range operations like hydro plants on different streams, cascaded hydro plants multi-chain hydro plants, and pumped storage hydro plants. This chapter also discusses the solution procedure for long-range generation scheduling of hydrothermal plants.
Chapter 5 provides the necessary background of multiobjective optimization and explains the various methods, namely weighting, ?-constraint, min-max, utility function and global criteria methods. Basic fuzzy set theory is also discussed in this chapter as required for decision making. The chapter elaborates on Surrogate Worth Trade-off approach for multiobjective thermal power dispatch and weighting method for (i) multiobjective thermal power dispatch, (ii) multiobjective thermal power dispatch considering active and reactive power balance, and (iii) multiobjective short-term hydrothermal scheduling.
Chapter 6 deals with multiobjective stochastic optimal power dispatch problems such as;
(i) multiobjective stochastic optimal thermal power dispatch using e-constraint method,
(ii) multiobjective stochastic optimal thermal power dispatch using Surrogate Worth Trade-off method, (iii) multiobjective stochastic optimal thermal power dispatch using weighting method, (iv) stochastic economic-emission load dispatch, (v) multiobjective thermal power dispatch using risk/dispersion method, (vi) stochastic multiobjective short-term hydrothermal scheduling, (vii) stochastic multiobjective long-term hydrothermal scheduling, and (viii) multiobjective thermal power dispatch using artificial neural networks (ANNs).
Chapter 7 provides an introduction to evolutionary programming technique for generation scheduling. Basics of genetic algorithm such as coding, genetic operators, random number generation are discussed in this chapter. The step-wise procedure to solve the economic dispatch problem using the genetic algorithm is also presented. Necessary appendices have been provided covering topics such as evaluation of expected values of used functions, evaluation of coefficient of variance of generator output, Kuhn-Tucker theorem, Newton-Raphson, Gauss elimination, Gauss-Seidel methods and Primal-Dual Interior Point method to solve the optimization problem.
We are indebted to our colleagues at Giani Zail Singh College of Engineering & Technology, Bathinda, and Indian Institute of Technology Delhi for their encouragement and various useful suggestions. We express our gratitude to Dr. S.C. Parti, Professor (Retd. ), TIET, Patiala for his constant interest and support. We hope this book will challenge the readers to delve into an insightful understanding of multiobjective optimization in power systems. We will welcome constructive criticism and appraisal by readers.
Contents:
Preface
1. Introduction
1.1 A Perspective
1.2 The Components of a Power System
1.3 Power System and Computers
1.4 Planning and Operating Problems
1.4.1 Resource and Equipment Planning
1.4.2 Operation Planning
1.4.3 Real-Time Operation
1.5 Artificial Intelligence and Neural Networks
1.6 Fuzzy Theory in Power Systems
References
2. Load Flow Studies
2.1 Introduction
2.2 Network Model Formulation
2.3 yBUS Formulation
2.3.1 No Mutual Coupling Between-Transmission Lines
2.3.2 Mutual Coupling Between Transmission Lines
2.4 Node Elimination in ZBUS
2.5 ZBUS Formulation
2.5.1 No Mutual Coupling Between Transmission Lines
2.5.2 Mutual Coupling Between Transmission Lines
2.6 Load Flow Problem
2.6.1 Slack Bus/Swing Bus/Reference Bus
2.6.2 PQ Bus/Load Bus
2.6.3 PV Bus/Generator Bus
2.6.4 Voltage-Controlled Buses
2.6.5 Limits
2.7 Computation of Line Flows
2.8 Modelling of Regulating Transformers
2.9 Gauss-Seidel Method
2.10 Mewton-Raphson Method
2.11 Decoupled Newton Method
2.12 Fast Decoupled Load Flow (FDLF)
2.13 Initial Guess for Load Flow
2.14 DC System Model
2.15 AC-DC Load Flow
2.16 Conclusion
References
3. Economic Load Dispatch of Thermal Generating Units
3.1 Introduction
3.2 Generator Operating Cost
3.3 Economic Dispatch Problem on a Bus Bar
3.3.1 Limit Constraint Fixing
3.4 Optimal Generation Scheduling
3.5 Economic Dispatch Using Newton-Raphson Method
3.6 Economic Dispatch Using the Approximate Newton-Raphson Method
3.7 Economic Dispatch Using Efficient Method
3.8 Classical Method to Calculate Loss Coefficients
3.9 Loss Coefficient Calculation Using bus
З.10 Loss Coefficients Using Sensitivity Factors
3.10.1 DC Load Row
3.10.2 Power Loss in a Line
3.10.3 Generation Shift Distribution (GSD) Factors
3.10.4 Generalized Generation Shift Distribution (GGSD) Factors
3.10.5 Derivation of GGDF
3.10.6 Evaluation of ^-Coefficients
3.11 Transmission Loss Coefficients
3.12 Transmission Loss Formula: Function of Generation and Loads
3.13 Economic Dispatch Using Exact Loss Formula
3.14 Economic Dispatch Using Loss Formula which is Function of
Real and Reactive Power
3.15 Economic Dispatch for Active and Reactive Power Balance
3.16 Evaluation of Incremental Transmission Loss
3.16.1 Alteative Method to Evaluate Incremental Loss
3.17 Economic Dispatch Based on Penalty Factors
3.18 Optimal Power Flow Based on Newton Method
3.18.1 Limits on Variables
3.18.2 Decoupled Method for Optimal Power Flow
3.19 Optimal Power Flow Based on Gradient Method
3.19.1 Inequality Constraints on Control Variables
3.19.2 Inequality Constraints on Dependent Variables
References
4. Optimal Hydrothermal Scheduling
4.1 Introduction
4.1.1 Classification of Hydro Plants
4.1.2 Long-Range Problem
4.1.3 Short-Range Problem
4.2 Hydro Plant Performance Models
4.2.1 Glimn-Kirchmayer Model
4.2.2 Hildebrand's Model
4.2.3 Hamilton-Lamonts's Model
4.2.4 Arvanitidis-Rosing Model
4.3 Short-Range Fixed-Head Hydrothermal Scheduling
4.3.1 Thermal Model
4.3.2 Hydro Model
4.3.3 Equality and Inequality Constraints
4.3.4 Transmission Losses
4.3.5 Discrete Form of Short-Range Fixed-Head Hydrothermal
Scheduling Problem
4.3.6 Initial Guess
4.3.7 Alteative Method for Initial Guess
4.4 Newton-Raphson Method for Short-Range Fixed-Head Hydrothermal
Scheduling
4.5 Approximate Newton-Raphson Method for Short-Range Fixed-Head Hydrothermal Scheduling
4.6 Short-Range Variable-Head Hydrothermal Scheduling – Classical Method
4.6.1 Thermal Model
4.6.2 Hydro Model
4.6.3 Reservoir Dynamics
4.6.4 Equality and Inequality Constraints
4.6.5 Transmission Losses
4.6.6 Discrete Form of Short-Range Variable-Head Hydrothermal
Scheduling Problem
4.6.7 Approximate Newton-Raphson Method for Thermal Generations
4.6.8 Initial Guess
4.7 Approximate Newton-Raphson Method for Short-Range Variable-Head Hydrothermal Scheduling
4.8 Hydro Plant Modelling for Long-Term Operation
4.8.1 Hydro Plants on Different Water Streams
4.8.2 Hydro Plants on the Same Water Stream
4.8.3 Multi-Chain Hydro Plants
4.8.4 Pumped Storage Plants
4.9 Long-Range Generation Scheduling of Hydrothermal Systems
4.9.1 Fuel Cost
4.9.2 Water Storage Equation
4.9.3 Hydro Generation
4.9.4 Power Balance Equation
4.9.5 Optimal Control Strategy
4.9.6 Direct Root Method
References
5. Multiobjective Generation Scheduling
5.1 Introduction
5.2 Multiobjective Optimization – State-of-the-Art
5.2.1 Weighting Method
5.2.2 Min-Max Optimum
5.2.3 e-Constraint Method [Haimes, 1977]
5.2.4 Weighted Min-Max Method [Charalambous, 1989]
5.2.5 Utility Function Method [Rao, 1987]
5.2.6 Global Criterion Method [Osyczka and Davies, 1984]
5.3 Fuzzy Set Theory in Power Systems
5.3.1 Basics of Fuzzy Set Theory
5.4 The Surrogate Worth Trade-off Approach for Multiobjective Thermal Power Dispatch Problem
5.4.1 Multiobjective Problem Formulation
5.4.2 The e-Constraint Method
5.4.3 The Surrogate Worth Trade-off (SWT) Function
5.4.4 Utility Function
5.4.5 Test System and Results
5.5 Multiobjective Thermal Power Dispatch Problem – Weighting Method
5.5.1 Decision Making
5.5.2 Sample System Study
5.6 Multiobjective Dispatch for Active and Reactive Power Balance
5.6.1 Sample System Study
5.7 Multiobjective Short-Range Fixed-Head Hydrothermal Scheduling – Approximate
Newton-Raphson Method
5.7.1 Sample System
References
6. Stochastic Multiobjective Generation Scheduling
6.1 Introduction
6.2 Multiobjective Stochastic Optimal Thermal Power Dispatch—
e-Constraint Method
6.2.1 Stochastic Problem Formulation
6.2.2 Algorithm
6.2.3 Application of the Method
6.3 Multiobjective Stochastic Optimal Thermal Power Dispatch—The Surrogate
Worth Trade-off Method
6.3.1 Multiobjective Optimization Problem Formulation
6.3.2 Solution Procedure
6.3.3 Surrogate Worth Trade-off Algorithm
6.3.4 Sample System Study
6.4 Multiobjective Stochastic Optimal Thermal Power Dispatch— Weighting Method
6.4.1 Stochastic Multiobjective Optimization Problem Formulation
6.4.2 Solution Approach
6.4.3 Decision Making
6.4.4 Results and Discussion
6.5 Stochastic Economic-Emission Load Dispatch
6.5.1 Stochastic Economic-Emission Problem Formulation
6.5.2 Solution Approach
6.5.3 Test System and Results
6.6 Multiobjective Optimal Thermal Power Dispatch—Risk/Dispersion Method
6.6.1 Multiobjective Optimization Problem Formulation
6.6.2 The e-Constraint Method
6.6.3 Parameter Sensitivity
6.6.4 Risk Index and Sensitivity Trade-offs
6.6.5 Test System and Results
6.7 Stochastic Multiobjective Short-Term Hydrothermal Scheduling
6.7.1 Stochastic Multiobjective Optimization Problem Formulation
6.7.2 Solution Procedure
6.7.3 Decision Making
6.7.4 Test Systems and Results
6.8 Stochastic Multiobjective Long-Term Hydrothermal Scheduling
6.8.1 Stochastic Multiobjective Optimization Problem Formulation
6.8.2 Optimal Control Strategy
6.8.3 Sample System Study
6.9 Multiobjective Thermal Power Dispatch Using Artificial Neural Network (ANN)
6.9.1 Stochastic Economic-Emission Problem Formulation
6.9.2 Membership Functions
6.9.3 Performance Index
6.9.4 Structure of ANN
6.9.5 Backpropagation Algorithm
6.9.6 Sample System Study
References
7. Evolutionary Programming for Generation Scheduling
7.1 Introduction
7.1.1 Coding
7.2 Fitness Function
7.3 Genetic Algorithm Operators
7.3.1 Reproduction
7.3.2 Competition and Selection
7.3.3 Crossover Operator
7.3.4 Mutation Random Numbers
7.4 Random Number Generation
7.6 Genetic Algorithm Solution Methodology
7.6.1 Encoding and Decoding
7.6.2 Calculation for Generation and Transmission Losses
7.6.3 Fitness Function and Parent Selection
7.7 Genetic Algorithm Solution Based on Real Power Search
7.7.1 Encoding and Decoding
7.7.2 Fitness Function and Parent Selection
References
Appendix A: Evaluation of Expected Operating Cost, NO^. Emission and
Power Losses Using Taylor's Series
Appendix B: Evaluation of a Coefficient of a Generator Output
Appendix C: Kuhn-Tucker Theorem
Appendix D: Newton-Raphson Method
Appendix E: Gauss Elimination Method
Appendix F: Primal-Dual Interior Point Method
Index
Preface
In response to increasing public awareness of the environmental situation and the plea for clean air, many engineers came up with new methods to reduce air pollution in parallel with pursuit of economy. Engineers are devoting considerable time to handle such conflicting situations through multiobjective optimization. The aim of multiobjective optimization is to help engineers (or decision makers) take the right decision in conflicting situations bedevilled with several objectives to be satisfied simultaneously. Further for large-scale integrated electric power systems, there is no other alteative but to use the digital computer as a computation tool for fast, accurate, and robust solution procedures.
This book is intended to serve as an introductory text to the topic of multiobjective optimization in electric power systems. It may also be used for self-study by practising personnel involved in planning and operation of thermal as well as integrated hydrothermal electric power systems. It has been the endeavour of the authors to provide simple and understandable basic computational algorithms so that students or practising engineers can develop their own programs in any high level language or improve the existing ones. Solved examples are given for better understanding of each power system problem discussed. The reader is expected to have a prior knowledge of basics of electric power system, optimization techniques, numerical methods, and matrix operations. The first chapter introduces the power system components, planning and operation problems, potential application of fuzzy theory and artificial neural networks in power systems.
Chapter 2 elaborates on power network modelling and important techniques of ac load flow analysis like Gauss-Seidel, Newton-Raphson, and decoupled load flow. To reduce the computation burden, initial guess for load flow is also explained. This chapter also deals with modelling and solution procedure for ac-dc load flow.
Chapter 3 is devoted to economic dispatch of thermal power systems. Newton-Raphson and approximations to Newton-Raphson method are discussed to solve the classical economic dispatch. The economic dispatch procedures are elaborated here to consider exact loss formula as well as real and reactive power balance. Rigorous economic dispatch techniques such as penalty factor method, gradient method, and Newton-Raphson method are discussed. The chapter also deals with the evaluation of Б-coefficients by classical method, F-bus method, and sensitivity factor method. It also explains the development of exact transmission loss formula.
Chapter 4 deals with the foundations of hydrothermal scheduling such as fixed-head, variable-head for short-term and long-term problems. It elaborates upon the classical Newton-Raphson and approximate Newton-Raphson methods to solve the fixed-head, short-range hydrothermal problem. Classical and approximate Newton-Raphson methods for short-range, variable-head, hydrothermal problems are also discussed in this chapter. It also deals with hydro plant modelling for long-range operations like hydro plants on different streams, cascaded hydro plants multi-chain hydro plants, and pumped storage hydro plants. This chapter also discusses the solution procedure for long-range generation scheduling of hydrothermal plants.
Chapter 5 provides the necessary background of multiobjective optimization and explains the various methods, namely weighting, ?-constraint, min-max, utility function and global criteria methods. Basic fuzzy set theory is also discussed in this chapter as required for decision making. The chapter elaborates on Surrogate Worth Trade-off approach for multiobjective thermal power dispatch and weighting method for (i) multiobjective thermal power dispatch, (ii) multiobjective thermal power dispatch considering active and reactive power balance, and (iii) multiobjective short-term hydrothermal scheduling.
Chapter 6 deals with multiobjective stochastic optimal power dispatch problems such as;
(i) multiobjective stochastic optimal thermal power dispatch using e-constraint method,
(ii) multiobjective stochastic optimal thermal power dispatch using Surrogate Worth Trade-off method, (iii) multiobjective stochastic optimal thermal power dispatch using weighting method, (iv) stochastic economic-emission load dispatch, (v) multiobjective thermal power dispatch using risk/dispersion method, (vi) stochastic multiobjective short-term hydrothermal scheduling, (vii) stochastic multiobjective long-term hydrothermal scheduling, and (viii) multiobjective thermal power dispatch using artificial neural networks (ANNs).
Chapter 7 provides an introduction to evolutionary programming technique for generation scheduling. Basics of genetic algorithm such as coding, genetic operators, random number generation are discussed in this chapter. The step-wise procedure to solve the economic dispatch problem using the genetic algorithm is also presented. Necessary appendices have been provided covering topics such as evaluation of expected values of used functions, evaluation of coefficient of variance of generator output, Kuhn-Tucker theorem, Newton-Raphson, Gauss elimination, Gauss-Seidel methods and Primal-Dual Interior Point method to solve the optimization problem.
We are indebted to our colleagues at Giani Zail Singh College of Engineering & Technology, Bathinda, and Indian Institute of Technology Delhi for their encouragement and various useful suggestions. We express our gratitude to Dr. S.C. Parti, Professor (Retd. ), TIET, Patiala for his constant interest and support. We hope this book will challenge the readers to delve into an insightful understanding of multiobjective optimization in power systems. We will welcome constructive criticism and appraisal by readers.
Contents:
Preface
1. Introduction
1.1 A Perspective
1.2 The Components of a Power System
1.3 Power System and Computers
1.4 Planning and Operating Problems
1.4.1 Resource and Equipment Planning
1.4.2 Operation Planning
1.4.3 Real-Time Operation
1.5 Artificial Intelligence and Neural Networks
1.6 Fuzzy Theory in Power Systems
References
2. Load Flow Studies
2.1 Introduction
2.2 Network Model Formulation
2.3 yBUS Formulation
2.3.1 No Mutual Coupling Between-Transmission Lines
2.3.2 Mutual Coupling Between Transmission Lines
2.4 Node Elimination in ZBUS
2.5 ZBUS Formulation
2.5.1 No Mutual Coupling Between Transmission Lines
2.5.2 Mutual Coupling Between Transmission Lines
2.6 Load Flow Problem
2.6.1 Slack Bus/Swing Bus/Reference Bus
2.6.2 PQ Bus/Load Bus
2.6.3 PV Bus/Generator Bus
2.6.4 Voltage-Controlled Buses
2.6.5 Limits
2.7 Computation of Line Flows
2.8 Modelling of Regulating Transformers
2.9 Gauss-Seidel Method
2.10 Mewton-Raphson Method
2.11 Decoupled Newton Method
2.12 Fast Decoupled Load Flow (FDLF)
2.13 Initial Guess for Load Flow
2.14 DC System Model
2.15 AC-DC Load Flow
2.16 Conclusion
References
3. Economic Load Dispatch of Thermal Generating Units
3.1 Introduction
3.2 Generator Operating Cost
3.3 Economic Dispatch Problem on a Bus Bar
3.3.1 Limit Constraint Fixing
3.4 Optimal Generation Scheduling
3.5 Economic Dispatch Using Newton-Raphson Method
3.6 Economic Dispatch Using the Approximate Newton-Raphson Method
3.7 Economic Dispatch Using Efficient Method
3.8 Classical Method to Calculate Loss Coefficients
3.9 Loss Coefficient Calculation Using bus
З.10 Loss Coefficients Using Sensitivity Factors
3.10.1 DC Load Row
3.10.2 Power Loss in a Line
3.10.3 Generation Shift Distribution (GSD) Factors
3.10.4 Generalized Generation Shift Distribution (GGSD) Factors
3.10.5 Derivation of GGDF
3.10.6 Evaluation of ^-Coefficients
3.11 Transmission Loss Coefficients
3.12 Transmission Loss Formula: Function of Generation and Loads
3.13 Economic Dispatch Using Exact Loss Formula
3.14 Economic Dispatch Using Loss Formula which is Function of
Real and Reactive Power
3.15 Economic Dispatch for Active and Reactive Power Balance
3.16 Evaluation of Incremental Transmission Loss
3.16.1 Alteative Method to Evaluate Incremental Loss
3.17 Economic Dispatch Based on Penalty Factors
3.18 Optimal Power Flow Based on Newton Method
3.18.1 Limits on Variables
3.18.2 Decoupled Method for Optimal Power Flow
3.19 Optimal Power Flow Based on Gradient Method
3.19.1 Inequality Constraints on Control Variables
3.19.2 Inequality Constraints on Dependent Variables
References
4. Optimal Hydrothermal Scheduling
4.1 Introduction
4.1.1 Classification of Hydro Plants
4.1.2 Long-Range Problem
4.1.3 Short-Range Problem
4.2 Hydro Plant Performance Models
4.2.1 Glimn-Kirchmayer Model
4.2.2 Hildebrand's Model
4.2.3 Hamilton-Lamonts's Model
4.2.4 Arvanitidis-Rosing Model
4.3 Short-Range Fixed-Head Hydrothermal Scheduling
4.3.1 Thermal Model
4.3.2 Hydro Model
4.3.3 Equality and Inequality Constraints
4.3.4 Transmission Losses
4.3.5 Discrete Form of Short-Range Fixed-Head Hydrothermal
Scheduling Problem
4.3.6 Initial Guess
4.3.7 Alteative Method for Initial Guess
4.4 Newton-Raphson Method for Short-Range Fixed-Head Hydrothermal
Scheduling
4.5 Approximate Newton-Raphson Method for Short-Range Fixed-Head Hydrothermal Scheduling
4.6 Short-Range Variable-Head Hydrothermal Scheduling – Classical Method
4.6.1 Thermal Model
4.6.2 Hydro Model
4.6.3 Reservoir Dynamics
4.6.4 Equality and Inequality Constraints
4.6.5 Transmission Losses
4.6.6 Discrete Form of Short-Range Variable-Head Hydrothermal
Scheduling Problem
4.6.7 Approximate Newton-Raphson Method for Thermal Generations
4.6.8 Initial Guess
4.7 Approximate Newton-Raphson Method for Short-Range Variable-Head Hydrothermal Scheduling
4.8 Hydro Plant Modelling for Long-Term Operation
4.8.1 Hydro Plants on Different Water Streams
4.8.2 Hydro Plants on the Same Water Stream
4.8.3 Multi-Chain Hydro Plants
4.8.4 Pumped Storage Plants
4.9 Long-Range Generation Scheduling of Hydrothermal Systems
4.9.1 Fuel Cost
4.9.2 Water Storage Equation
4.9.3 Hydro Generation
4.9.4 Power Balance Equation
4.9.5 Optimal Control Strategy
4.9.6 Direct Root Method
References
5. Multiobjective Generation Scheduling
5.1 Introduction
5.2 Multiobjective Optimization – State-of-the-Art
5.2.1 Weighting Method
5.2.2 Min-Max Optimum
5.2.3 e-Constraint Method [Haimes, 1977]
5.2.4 Weighted Min-Max Method [Charalambous, 1989]
5.2.5 Utility Function Method [Rao, 1987]
5.2.6 Global Criterion Method [Osyczka and Davies, 1984]
5.3 Fuzzy Set Theory in Power Systems
5.3.1 Basics of Fuzzy Set Theory
5.4 The Surrogate Worth Trade-off Approach for Multiobjective Thermal Power Dispatch Problem
5.4.1 Multiobjective Problem Formulation
5.4.2 The e-Constraint Method
5.4.3 The Surrogate Worth Trade-off (SWT) Function
5.4.4 Utility Function
5.4.5 Test System and Results
5.5 Multiobjective Thermal Power Dispatch Problem – Weighting Method
5.5.1 Decision Making
5.5.2 Sample System Study
5.6 Multiobjective Dispatch for Active and Reactive Power Balance
5.6.1 Sample System Study
5.7 Multiobjective Short-Range Fixed-Head Hydrothermal Scheduling – Approximate
Newton-Raphson Method
5.7.1 Sample System
References
6. Stochastic Multiobjective Generation Scheduling
6.1 Introduction
6.2 Multiobjective Stochastic Optimal Thermal Power Dispatch—
e-Constraint Method
6.2.1 Stochastic Problem Formulation
6.2.2 Algorithm
6.2.3 Application of the Method
6.3 Multiobjective Stochastic Optimal Thermal Power Dispatch—The Surrogate
Worth Trade-off Method
6.3.1 Multiobjective Optimization Problem Formulation
6.3.2 Solution Procedure
6.3.3 Surrogate Worth Trade-off Algorithm
6.3.4 Sample System Study
6.4 Multiobjective Stochastic Optimal Thermal Power Dispatch— Weighting Method
6.4.1 Stochastic Multiobjective Optimization Problem Formulation
6.4.2 Solution Approach
6.4.3 Decision Making
6.4.4 Results and Discussion
6.5 Stochastic Economic-Emission Load Dispatch
6.5.1 Stochastic Economic-Emission Problem Formulation
6.5.2 Solution Approach
6.5.3 Test System and Results
6.6 Multiobjective Optimal Thermal Power Dispatch—Risk/Dispersion Method
6.6.1 Multiobjective Optimization Problem Formulation
6.6.2 The e-Constraint Method
6.6.3 Parameter Sensitivity
6.6.4 Risk Index and Sensitivity Trade-offs
6.6.5 Test System and Results
6.7 Stochastic Multiobjective Short-Term Hydrothermal Scheduling
6.7.1 Stochastic Multiobjective Optimization Problem Formulation
6.7.2 Solution Procedure
6.7.3 Decision Making
6.7.4 Test Systems and Results
6.8 Stochastic Multiobjective Long-Term Hydrothermal Scheduling
6.8.1 Stochastic Multiobjective Optimization Problem Formulation
6.8.2 Optimal Control Strategy
6.8.3 Sample System Study
6.9 Multiobjective Thermal Power Dispatch Using Artificial Neural Network (ANN)
6.9.1 Stochastic Economic-Emission Problem Formulation
6.9.2 Membership Functions
6.9.3 Performance Index
6.9.4 Structure of ANN
6.9.5 Backpropagation Algorithm
6.9.6 Sample System Study
References
7. Evolutionary Programming for Generation Scheduling
7.1 Introduction
7.1.1 Coding
7.2 Fitness Function
7.3 Genetic Algorithm Operators
7.3.1 Reproduction
7.3.2 Competition and Selection
7.3.3 Crossover Operator
7.3.4 Mutation Random Numbers
7.4 Random Number Generation
7.6 Genetic Algorithm Solution Methodology
7.6.1 Encoding and Decoding
7.6.2 Calculation for Generation and Transmission Losses
7.6.3 Fitness Function and Parent Selection
7.7 Genetic Algorithm Solution Based on Real Power Search
7.7.1 Encoding and Decoding
7.7.2 Fitness Function and Parent Selection
References
Appendix A: Evaluation of Expected Operating Cost, NO^. Emission and
Power Losses Using Taylor's Series
Appendix B: Evaluation of a Coefficient of a Generator Output
Appendix C: Kuhn-Tucker Theorem
Appendix D: Newton-Raphson Method
Appendix E: Gauss Elimination Method
Appendix F: Primal-Dual Interior Point Method
Index