POIilDK SYSTDM OPTIMIZATION

Transcription

1 POIilDK SYSTDM OPTIMIZATION trlndlniirftlfifdrsl D.P. KOTITARI. J.S. DHILLON E* Power system optimization is intended to introduce the methods of multi-objective optimization in integrated electric power system operation, covering economrc, environmental, security and risk aspects as well. Evolutionary algorithms-which mimic natural evolutionary principles to constitute random search and optimization procedures are appended in this new edition to solve generation scheduling problems. written in a student-friendly style, the book provides simple and understandable basic computational concepts and algorithms used in generation scheduling so that the readers can develop their own programs in any highlevel programming linguage. This clear, logical overview of generation scheduling in electric power systehs plrmits both students and power engineers to understand and apply optimization on a dependable basis. The book is particularly easy-to-use with sound and consistenterminology and perspective throughout. This edition presents systematic coverage of local and global optimization techniques such as binary- and real-coded genetic algorithms, evolutionary algorithms, particle swarm optimization and differential evolutionary algorithms. The economic dispatch problem presented, considers higher-order nonlinearities and discontinuities in inputoutput characteristics in fossil fuel burning plants due to valve-point loading, ramprate limits and prohibited operating zones. search optimization techniques piesented are those which participate efficiently in decision making to solve the multiobjective optimization problems. stochastic optimal generation scheduling is also updated in the new edition. Generalized Z-bus distribution factors (GZBDF) are presented to compute the active and reactive power flow on transmission lines. The interactive decision making methodology based on tuzzy set theory, in order to determine the optimal generation allocation to committed generating units, is also discussed. This book is intended to meet the needs of a diverse range of groups interested in the application of optimization techniques to power system operation. lt requires onry an elementary knowledge of numerical techniques and matrix operation to understand most of the topics. lt is designed to serve as a textbook for postgraduate electrical engineering students, as well as a reference for faculty, researchers, and power engineers interested in the use of optimization as a tool for reliable and secure economic operation of power systems.

2 The book discusses: o Load flow techniques and economic dispatch-both classical and.rigorous i Eionomic Oispatch considering valve-point loading, ramp-rate limits and prohibited operating zones o ieal coded genetic -programming algorithms for economic dispatch o Evolutionary for economic. dispatch. o Particle swarm optimization for economlc olspalcn. Ditferential evoluiionary algorithm for economic disp.atch o Stochastic multiobjective thermal power dispatch w-ith security c Generalized Z-bui distribution factors lo compute line flow e Stochastic multiobiective hydrothermal generation.scheduling r Muttiobiective ther'mal powbr dispatch u-sing artificial neural networks c Fuzzy multiobiective generation scheduling. Multiobiective generation scheduling by.e"t.hing *"ight p"fi F D.P. KOTHARI, Ph.D., is Vice Chancellor of VIT University,!e-!org. Earlier' he was Frotessor at the centie for Energy studies, lndian Institute of Technology Delhi. He also served as Director-in-Chargd, llt Delhi (2005), Deputy Director (Administration), iii olini (2003-oo), Principal, National (1se7-1se8) lqstlrlg.9f.-tech.nolggv-.1tt"gpql ano-heiol Centre'ior Energy Studies, llt Delhi ( ). Dr. Kothari's fields of specialization include optimal-hydro-thermal scheduling, unit commitment, maintenance sbheduling, energy cohservati'on, and power quality.and energy systems planning ino-roodtiing. A"iecipient of several national awards, Dr. Kothari-who contributed extenjivety to" the spdcialized areas, guided -28 Ph.D.s and 60 M.Tech.s, authored io Ooot<sbn Power'systems and pubiished 625 research papers in various national and international journals. J,S. DHILLON, Ph.D., is Professor, Department of Electrical and Instrumentation Engineering, sant Longowal Institute. of Engineering and Technology, Longowal, where fre"also seiied as the-head ol the department (from 2OO2 Io 2005)' Earlier he served as Assistant Professor ( ) Giani Zail singh college of -Ergineering and iechnofogy, Bathinda anb Lecturer ( ), Thapar Institute. ol Engineering and fecnnotody, patiala. professor Dhillon has published/pre.sented 91 research papers in various niiional and international journals/conferences. His research interests include microprocei"or applications, multi6bjective thermal.dispatch, hydrothermal scheduling' neural networks, tuzzy set theory and soft computing applications in power systems' Preface. Preface to the First Edition 1. Introduction 2. Load Flow Studies 3. Economic Load Dispatch of Thermal Generating Units 4. Optimal Hydrothermal Scheduling-, 5. Mfuftiob;eciive Generation Scheduling^ Stocha6tic Multiobiective Generation Scheduling Evolutionary Progiamming lor Generation Scheduling ^ 8. Multiobiectiire Ge-neration Schedulingl Weight Pattern Search Appendices. lndex Multi Colour Services 09/2010

3 POWER SYSTEM OPTIMIZATION SECOND EDITION D.P. KOTHARI Vice Chancellor VIT University Vellore and Former Director-in-Charge Indian Institute of Technology Delhi New Delhi J.S. DHILLON Professor Department of Electrical and Instrumentation Engineering Sant Longowal Institute of Engineering and Technology (Deemed-to-be-University) Longowal, Punjab New Delhi

4 Contents Preface... xi Preface to the First Edition... xiii 1. Introduction A 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 Evolutionary Algorithms... 7 References Load Flow Studies Introduction Network Model Formulation Y BUS Formulation No Mutual Coupling between Transmission Lines Mutual Coupling between Transmission Lines Node Elimination in Z BUS Z BUS 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 v

5 vi Contents 2.7 Computation of Line Flows Modelling of Regulating Transformers Gauss Seidel Method Newton Raphson Method Decoupled Newton Method Fast Decoupled Load Flow (FDLF) Initial Guess for Load Flow DC System Model AC DC Load Flow Conclusion References 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 Y BUS Loss Coefficients Using Sensitivity Factors DC Load Flow Power Loss in a Line Generation Shift Distribution (GSD) Factors Generalized Generation Shift Distribution (GGSD) Factor Derivation of GGDF Evaluation of B-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 References

6 Contents vii 4. Optimal Hydrothermal Scheduling Introdcution 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 Hydrothermal 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 References

7 viii Contents 5. 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 References 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

8 Contents ix 6.5 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 References Evolutionary Programming for Generation Scheduling Introduction Coding Fitness Function Genetic Algorithm Operators Reproduction Competition and Selection Crossover Operator Mutation Random Number Generation Economic Dispatch Problem 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 Selection Economic Dispatch with Valve Point Loading

9 x Contents 7.9 Economic Dispatch with Ramp Rate Limits and Prohibited Operating Zones Prohibited Operating Zone Ramp Rate Limit Evolutionary Search Method for Economic Dispatch Evolutionary Search Optimization Method Evolutionary Programming for Economic Dispatch I Evolutionary Programming for Economic Dispatch II Particle Swarm Optimization for Economic Dispatch Anti-Predatory Particle Swarm Optimization Differential Evolution for Economic Dispatch Real Coded Genetic Algorithm References Multiobjective Generation Scheduling: Weight Pattern Search Introduction Economic Emission Load Dispatch Multiobjective Optimization Problem Formulation Operating Limits Membership Functions of Objectives Weightage Pattern Search: Evolutionary Search Method Weightage Pattern Search: Genetic Algorithm Test Systems and Results Comparison of Results Multiobjective Secure Load Dispatch Power Flow on Transmission Lines Generalized Z-Bus Distribution Factors (GZBDF) Multiobjective Optimization Problem Formulation Solution Procedure Sample Study System Results and Discussion Stochastic Multiobjective Optimal Generation Allocation Stochastic Multiobjective Optimization Problem Formulation Solution Approach Test System and Results Fuzzy Multiobjective Secure Generation Scheduling Fuzzy Multiobjective Optimization Problem Formulation Generation Search with Genetic Algorithm Results and Discussions References Appendix A: Evaluation of the Expected Values of Functions 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