Ebook: Power System Optimization

2007. , 572 pages. The same problems considered, but different methodology approach in comparison with soviet/russian electric power school (Venikov, Sovalov, Gornstein, 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 alternative 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:Chapter I
Introduction
Perspective
The Components of a Power System
Power System and Computers
Planning and Operating Problems
Resource and Equipment Planning
Operation Planning
Real-Time Operation
Artificial Intelligence and Neural Networks
Fuzzy Theory in Power Systems
Chapter II
Load Flow Studies
Introduction
Network Model Formulation
yBUS Formulation
No Mutual Coupling Between-Transmission Lines
Mutual Coupling Between Transmission Lines
Node Elimination in ZBUS
ZBUS Formulation
No Mutual Coupling Between Transmission Lines
Mutual Coupling Between Transmission Lines
Load Flow Problem
Slack Bus/Swing Bus/Reference Bus
PQ Bus/Load Bus
PV Bus/Generator Bus
Voltage-Controlled Buses
Limits
Computation of Line Flows
Modelling of Regulating Transformers
Gauss-Seidel Method
Mewton-Raphson Method
Decoupled Newton Method
Fast Decoupled Load Flow (FDLF)
Initial Guess for Load Flow
DC System Model
AC-DC Load Flow
Conclusion
Chapter III
Economic Load Dispatch of Thermal Generating Units
Introduction
Generator Operating Cost
Economic Dispatch Problem on a Bus Bar
Limit Constraint Fixing
Optimal Generation Scheduling
Economic Dispatch Using Newton-Raphson Method
Economic Dispatch Using the Approximate Newton-Raphson Method
Economic Dispatch Using Efficient Method
Classical Method to Calculate Loss Coefficients
Loss Coefficient Calculation Using bus
Loss Coefficients Using Sensitivity Factors
DC Load Row
Power Loss in a Line
Generation Shift Distribution (GSD) Factors
Generalized Generation Shift Distribution (GGSD) Factors
Derivation of GGDF
Evaluation of ^-Coefficients
Transmission Loss Coefficients
Transmission Loss Formula: Function of Generation and Loads
Economic Dispatch Using Exact Loss Formula
Economic Dispatch Using Loss Formula which is Function of Real and Reactive Power
Economic Dispatch for Active and Reactive Power Balance
Evaluation of Incremental Transmission Loss
Alternative Method to Evaluate Incremental Loss
Economic Dispatch Based on Penalty Factors
Optimal Power Flow Based on Newton Method
Limits on Variables
Decoupled Method for Optimal Power Flow
Optimal Power Flow Based on Gradient Method
Inequality Constraints on Control Variables
Inequality Constraints on Dependent Variables
Chapter IV
Optimal Hydrothermal Scheduling
Introduction
Classification of Hydro Plants
Long-Range Problem
Short-Range Problem
Hydro Plant Performance Models
Glimn-Kirchmayer Model
Hildebrand's Model
Hamilton-Lamonts's Model
Arvanitidis-Rosing Model
Short-Range Fixed-Head Hydrothermal Scheduling
Thermal Model
Hydro Model
Equality and Inequality Constraints
Transmission Losses
Discrete Form of Short-Range Fixed-Head Hydrothermal Scheduling Problem
Initial Guess
Alternative Method for Initial Guess
Newton-Raphson Method for Short-Range Fixed-Head Hydrothermal Scheduling
Approximate Newton-Raphson Method for Short-Range Fixed-Head Hydrothermal Scheduling
Short-Range Variable-Head Hydrothermal Scheduling – Classical Method
Thermal Model
Hydro Model
Reservoir Dynamics
Equality and Inequality Constraints
Transmission Losses
Discrete Form of Short-Range Variable-Head Hydrothermal Scheduling Problem
Approximate Newton-Raphson Method for Thermal Generations
Initial Guess
Approximate Newton-Raphson Method for Short-Range Variable-Head Hydrothermal Scheduling
Hydro Plant Modelling for Long-Term Operation
Hydro Plants on Different Water Streams
Hydro Plants on the Same Water Stream
Multi-Chain Hydro Plants
Pumped Storage Plants
Long-Range Generation Scheduling of Hydrothermal Systems
Fuel Cost
Water Storage Equation
Hydro Generation
Power Balance Equation
Optimal Control Strategy
Direct Root Method
Chapter V
Multiobjective Generation Scheduling Introduction
Multiobjective Optimization – State-of-the-Art
Weighting Method
Min-Max Optimum
e-Constraint Method [Haimes, 1977]
Weighted Min-Max Method [Charalambous, 1989]
Utility Function Method [Rao, 1987]
Global Criterion Method [Osyczka and Davies, 1984]
Fuzzy Set Theory in Power Systems
Basics of Fuzzy Set Theory
The Surrogate Worth Trade-off Approach for Multiobjective Thermal Power Dispatch Problem
Multiobjective Problem Formulation
The e-Constraint Method
The Surrogate Worth Trade-off (SWT) Function
Utility Function
Test System and Results
Multiobjective Thermal Power Dispatch Problem – Weighting Method
Decision Making
Sample System Study
Multiobjective Dispatch for Active and Reactive Power Balance
Sample System Study
Multiobjective Short-Range Fixed-Head Hydrothermal Scheduling – Approximate Newton-Raphson Method
Sample System
Chapter VI
Stochastic Multiobjective Generation Scheduling
Introduction
Multiobjective Stochastic Optimal Thermal Power Dispatch—e-Constraint Method
Stochastic Problem Formulation
Algorithm
Application of the Method
Multiobjective Stochastic Optimal Thermal Power Dispatch—The Surrogate Worth Trade-off Method
Multiobjective Optimization Problem Formulation
Solution Procedure
Surrogate Worth Trade-off Algorithm
Sample System Study
Multiobjective Stochastic Optimal Thermal Power Dispatch— Weighting Method
Stochastic Multiobjective Optimization Problem Formulation
Solution Approach
Decision Making
Results and Discussion
Stochastic Economic-Emission Load Dispatch
Stochastic Economic-Emission Problem Formulation
Solution Approach
Test System and Results
Multiobjective Optimal Thermal Power Dispatch—Risk/Dispersion Method
Multiobjective Optimization Problem Formulation
The e-Constraint Method
Parameter Sensitivity
Risk Index and Sensitivity Trade-offs
Test System and Results
Stochastic Multiobjective Short-Term Hydrothermal Scheduling
Stochastic Multiobjective Optimization Problem Formulation
Solution Procedure
Decision Making
Test Systems and Results
Stochastic Multiobjective Long-Term Hydrothermal Scheduling
Stochastic Multiobjective Optimization Problem Formulation
Optimal Control Strategy
Sample System Study
Multiobjective Thermal Power Dispatch Using Artificial Neural Network (ANN)
Stochastic Economic-Emission Problem Formulation
Membership Functions
Performance Index
Structure of ANN
Backpropagation Algorithm
Sample System Study
Chapter VII
Evolutionary Programming for Generation Scheduling
Introduction
Coding
Fitness Function
Genetic Algorithm Operators
Reproduction
Competition and Selection
Crossover Operator
Mutation Random Numbers
Random Number Generation
Genetic Algorithm Solution Methodology
Encoding and Decoding
Calculation for Generation and Transmission Losses
Fitness Function and Parent Selection
Genetic Algorithm Solution Based on Real Power Search
Encoding and Decoding
Fitness Function and Parent SelectionAppendix 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