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Contributors to Tutorial on, Fuzzy Logic Applications in Power Systems by Chapter. M Y Chow North Carolina State University,K Tomsovic Washington State University. K Butler Texas A M University, G L Torres Escola Federal de Engenharia de Itajuba. O P Malik University of Calgary,D Niebur Drexel University. T Hiyama Kumamoto University,K Y Lee Pennsylvania State University.

J Momoh Howard University,D Srinivasan National University of Singapore. K Tomsovic Washington State University,B Baer Seimens Empros. M Y Chow North Carolina State University,P Luh University of Conneticut. S Lin University of Conneticut,J Zhu North Carolina State University. H Sasaki Hiroshima University,R Yokoyama Tokyo Metropolitan University.

J Kubokawa Hiroshima University,H Mori Meiji University. Table of Contents,TABLE OF CONTENTS III,CHAPTER 1 OVERVIEW 1 1. A REFERENCES 1,CHAPTER 2 FUZZY SET FUNDAMENTALS 2 1. A FUZZY SETS 2 1, A 1 Membership Functions Fundamental Definitions 2 1. A 2 Set Operations 2 1,A 3 Defining Fuzzy Sets 2 2.

B EXPERT REASONING AND APPROXIMATE REASONING 2 2,B 1 Fuzzy Measures 2 2. B 2 Approximate Reasoning 2 3,B 3 The Role of Linguistic Variables 2 3. B 4 Fuzzy Propositions 2 3,B 5 Fuzzy Implication 2 4. B 6 Correlation Methods 2 5,B 7 Aggregation 2 5,B 8 Methods of Defuzzification 2 5. C FUZZY OPTIMIZATION 2 6,C 1 Initial Considerations 2 6.

C 2 Fuzzy Optimization by Pseudogoal Function 2 7,C 3 Fuzzy Programming 2 9. C 4 Fuzzy Multi Criteria Analysis 2 9,D FUZZY CONTROL 2 13. D 1 Initial Considerations 2 13,D 2 Brief Description of the Software 2 13. D 3 Brief Description of the Software 2 13,D 4 Illustrative Examples 2 14. REFERENCES 2 14,CHAPTER 3 CONTROL APPLICATIONS 3 1.

A INTRODUCTION TO POWER SYSTEM CONTROL 3 1,A 1 Motivation 3 1. A 2 Power System Control Tasks 3 1,B FUZZY SYSTEMS 3 2. B 1 Review of Basic Concepts 3 2,B 2 Fuzzy Basis Functions 3 5. C STATE OF THE ART OF FUZZY CONTROL FOR POWER SYSTEMS 3 7. D APPLICATION OF A FUZZY LOGIC CONTROLLER AS A POWER SYSTEM STABILIZER 3 7. E A SELF LEARNING FUZZY POWER SYSTEM STABILIZER 3 9. F FIELD STUDIES OF A FUZZY LOGIC POWER SYSTEM STABILIZER 3 10. F 1 Simulation Studies 31 8 9 3 10, F 2 Experimental Studies on 5kVA Laboratory System 13 3 10. F 3 Site Tests in October 1992 32 3 11, F 4 Evaluation on Analog Power System Simulator 10 3 11.

F 5 Long Term Evaluation of PC Based Prototype 10 3 11. F 6 Permanent Installation after Disturbance Tests 3 11. G CONCLUSIONS 3 12,H REFERENCES 3 12,CHAPTER 4 CONTROL DESIGN AND STABILITY 4 1. A CONTROL DESIGN TECHNIQUES 4 1,A 1 Fixed Fuzzy Controller Design 4 1. A 2 Adaptive Fuzzy Controller Design 4 8,B TUNING CONTROLLER PERFORMANCE 4 10. B 1 Automatic Tuning of Fuzzy Logic Controller 4 10. B 2 Self Organizing Fuzzy Controller Design 4 12,C REFERENCES 4 12. CHAPTER 5 EXPERT SYSTEM APPLICATIONS 5 1,A EXPERT SYSTEMS 5 1.

A 1 Desirable Expert System Features 5 1, A 2 Suitable Application Areas for Expert Systems 5 2. A 3 Expert System Applications 5 2, B REASONING WITH UNCERTAINTY IN RULE BASED EXPERT SYSTEMS 5 3. B 1 Subjective Probability and Statistics 5 4,B 2 Measures of Belief and Disbelief 5 5. B 3 Certainty Factors 5 5,B 4 Fuzzy Logic 5 6,C EXAMPLE APPLICATION FAULT DIAGNOSIS 5 7. C 1 Problem Statement 5 7,C 2 Structure of the Fault Diagnosis System 5 7.

C 3 Island Identification 5 8,C 4 Fault Section Identification 5 8. D CONCLUSION 5 10,E REFERENCES 5 10,CHAPTER 6 OPTIMIZATION TECHNIQUES I 6 1. A SESSION OVERVIEW 6 1, B BRIEF OVERIVEW OF YEGER S MULTI OBJECTIVE DECISION MAKING AND LINEAR FUZZY LINEAR PROGRAMMING 6 1. B 1 Yager s Fuzzy Logic Multi Objective Decision Making Scheme 6 1. B 2 Fuzzy Linear Programming 6 2, C APPLICATION OF FUZZY OPTIMIZATION METHODS TO POWER SYSTEM APPLICATIONS 6 3. C 1 Application of Yager s Fuzzy Multi objective Optimization Method for Power Distribution System Spatial Load. Forecasting 6 3,C 2 References 6 6, D APPLICATION OF FUZZY LINEAR PROGRAMMING WITH LAGRANGIAN RELAXATION TECHNIQUE TO POWER SCHEDULING.

AND TRANSACTIONS 6 7, D 1 Scheduling and Transactions in an Uncertain Environment 6 7. D 2 Problem Formulation 6 7,D 3 Solution Methodology 6 8. D 4 Numerical Testing Results 6 9,D 5 References 6 10. CHAPTER 7 OPTIMIZATION TECHNIQUES II 7 1, A GENERATION EXPANSION PROBLEM BY MEANS OF MULTI OBJECTIVE FUZZY OPTIMIZATION 7 1. A 1 Introduction 7 1,A 2 Fuzzy Linear Programming 7 2.

A 3 Formulation of Generation Expansion Planning 7 3. A 4 Discussions on Numerical Simulations 7 5,A 5 Concluding Remarks 7 8. A 6 References 7 8, B A SOLUTION METHOD OF MULTI OBJECTIVE OPTIMAL POWER FLOW BY MEANS OF FUZZY COORDINATION 7 8. B 1 Introduction 7 8,B 2 Multi objective Optimal Power Flow 7 9. B 3 Interactive Fuzzy Multi objective Optimal Power Flow 7 10. B 4 Solution Algorithms 7 11,B 5 Application to the Test System 7 12. B 6 Discussions and Concluding Remarks 7 12,B 7 References 7 12.

CHAPTER 8 HYBRID TECHNIQUES IN FUZZY LOGIC 8 1,A INTRODUCTION 8 1. B SOFT COMPUTING 8 1,C TYPICAL NEURO FUZZY MODELS 8 2. C 1 Type A 8 2,C 2 Type B 8 2,C 3 Types C D 8 2,C 4 Type E 8 2. C 5 Type F 8 2,C 6 Type G 8 2,C 7 Type H 8 2,C 8 Type I 8 3. C 9 Type J 8 3,C 10 Type K 8 3, D TYPICAL APPLICATIONS OF NEURO FUZZY MODELS TO POWER SYSTEMS 8 3.

E CONCLUSIONS 8 5,F REFERENCES 8 5,G APPENDIX 8 6,Chapter 1 Overview. This tutorial provides attendees with a comprehensive are four approaches to the developing fuzzy rules 7 1. overview of fuzzy logic applications in power systems extract from expert experience and control engineering. Every effort was made to ensure the material was self knowledge 2 observe the behavior of human operators 3. contained and requires no specific experience in fuzzy logic use a fuzzy model of a process and 4 learn relationships. methods At the same time this booklet includes through experience or simulation with a learning process. contributions which are undoubtedly state of the art These approaches do not have to be mutually exclusive. research Thus it is hoped that practitioners at all levels will Due to the use of linguistic variables and fuzzy rules the. find useful information here Fuzzy logic technology has system can be made understandable to a non expert operator. achieved impressive success in diverse engineering In this way fuzzy logic can be used as a general. applications ranging from mass market consumer products to methodology to incorporate knowledge heuristics or theory. sophisticated decision and control problems 1 into controllers and decision makers. Applications within power systems are extensive with more. than 100 archival publications in a recent survey 2 3 This tutorial begins with a general section on fuzzy logic. Several of these applications have found their way into techniques and methods Simplified examples are used to. practice and fuzzy logic methods are becoming another highlight the fundamental methodologies Control. important approach for practicing engineers to consider applications are addressed in chapters 3 and 4 Chapter 3. provides fundamental analysis as well as a brief description. In 1965 L A Zadeh laid the foundations of fuzzy set theory of a controller in field use Chapter 4 presents more. 4 as a method to deal with the imprecision of practical advanced concepts including both control design and. systems Bellman and Zadeh write Much of the decision stability analysis useful for the more experienced developer. making in the real world takes place in an environment in Approaches based on approximate reasoning in expert. which the goals the constraints and the consequences of systems are presented in Chapter 5 with a specific. possible actions are not known precisely 5 This application to diagnostic systems This is followed by two. imprecision or fuzziness is the core of fuzzy sets or fuzzy extensive chapters on optimization problems Chapter 6. logic applications Fuzzy sets were proposed as a presents applications in spatial load forecasting and in. generalization of conventional set theory Partially as result scheduling Applications on generation expansion planning. of this fact fuzzy logic remained the purview of highly and optimal power flow in Chapter 7 highlight an alternative. specialized and mathematical technical journals for many approach to optimization The tutorial concludes with a. years This changed abruptly with the highly visible success chapter on advanced applications including hybrid. of several control applications in the late 1980s applications of neural nets and fuzzy logic. Heuristics intuition expert knowledge experience and A References. linguistic descriptions are obviously important to power. 1 M Y Chow Fuzzy Systems in CRC Press Industrial, engineers Virtually any practical engineering problem Electronics Handbook D Irwin Ed CRC 1996. requires some imprecision in the problem formulation and 2 J Zhu and M Y Chow A Review of Emerging Techniques on. subsequent analysis For example distribution system Generation Expansion Planning IEEE Transactions on Power. planners rely on spatial load forecasting simulation programs Systems in press. to provide information for a variety of planning scenarios 6 3 J A Momoh X W Ma and K Tomsovic Overview and. Linguistic descriptions of growth patterns such as close by Literature Survey of Fuzzy Set Theory in Power Systems. or fast and design objectives such as prefer or reduce are IEEE Transactions on Power Systems Vol 10 No 3 Aug. imprecise in nature The conventional engineering 1995. 4 L A Zadeh Fuzzy Sets in Information and Control vol 8. formulations do not capture such linguistic and heuristic New York Academic Press 1965 pp 338 353. knowledge in an effective manner 5 R E Bellman and L A Zadeh Decision making in a fuzzy. environment Management Science vol 17 pp 141 164, Fuzzy logic implements human experiences and preferences 1970. via membership functions and fuzzy rules Fuzzy 6 M Y Chow and H Tram Applications of Fuzzy Logic. membership functions can have different shapes depending Technology for Spactial Load Forecasting IEEE Transactions. on the designer s preference and or experience The fuzzy on Power Systems 1996 in press. rules which describe relationships at a high level in a 7 M Y Chow and A Menozzi Design Methodology of an. linguistic sense are typically written as antecedent Intelligent Controller Using Artificial Neural Networks. presented at IECON 93 Maui Hawaii 1993, consequent pairs of IF THEN statements Basically there. Chapter 2 Fuzzy Set Fundamen tals, A Fuzzy Sets When X is an interval of real numbers a fuzzy set A is.

expressed as, Zadeh makes a case that humans reason not in terms of. discrete symbols and numbers but in terms of fuzzy sets 1 m A x. These fuzzy terms define general categories but not rigid x. fixed collections The transition from one category concept. idea or problem state to the next is gradual with some states An empty fuzzy set has an empty support which implies that. having greater or less membership in the one set and then the membership function assigns 0 to all elements of the. another From this idea of elastic sets Zadeh proposed the universal set. concept of a fuzzy set Fuzzy sets are functions that map a A technical concept closely related to the support set is the. value that might be a member of the set to a number between alpha level set or the a cut An alpha level is a threshold. zero and one indicating its actual degree of membership A restriction on the domain of the fuzzy set based on the. degree of zero means that the value is not in the set and a membership grade of each domain value This set A is the. degree of one means that the value is completely a cut of A which contains all the domain values that are part. representative of the set This produces a curve across the of the fuzzy set at a minimum membership value of a. members of the set There are many books that have been There are two kinds of a cuts weak and strong The weak. written on the subject of fuzzy sets since Zadeh introduced. a cut is defined as Aa x X mA x a and the strong,the fuzzy set concept in 1965 1 19. cut as Aa x X mA x a Also the alpha level set, describes a power or strength function that is used by fuzzy. A 1 Membership Functions Fundamental Definitions, models to decide whether or not a truth value should be. considered equivalent to zero This is an important facility. Let X be a set of objects called the universe whose elements that controls the execution of fuzzy rules as well as the. are denoted x Membership in a subset A of X is the intersection of multiple fuzzy sets. membership function mA from X to the real interval 0 1. The universe is all the possible elements of concern in the The degree of membership is known as the membership or. particular context A is called a fuzzy set and is a subset of X truth function since it establishes a one to one. that has no sharp boundary mA is the grade of membership x correspondence between an element in the domain and a. in A The closer the value of mA is to 1 the more x belongs truth value indicating its degree of membership in the set It. to A The total allowable universe of values is called the takes the form. domain of the fuzzy set The domain is a set of real numbers. systems Bellman and Zadeh write Much of the decision making in the real world takes place in an environment in which the goals the constraints and the consequences of possible actions are not known precisely 5 This imprecision or fuzziness is the core of fuzzy sets or fuzzy logic applications Fuzzy sets were proposed as a

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