Tutorial on Evolutionary Techniques and Fuzzy Logic in Power Systems Prepared for the IEEE-PES Summer Meeting in Seattle July, 2000 Course Coordinator: Mohamed A. El-Sharkawi, University of Washington Contributors: Chapter 1: Theory of Evolutionary Computation Russel Eberhart, Purdue School of Engineering and Technology, Indiana University Purdue University Indianapolis Chapter 2: An Introduction to Fuzzy Inference Robert J. Marks, University of Washington Chapter 3: Application of Evolutionary Technique to Power System Security Assessment Craig Jensen, Microsoft Corporation M. A. El-Sharkawi, University of Washington Robert J. Marks, University of Washington Chapter 4: Application of EC to Optimization, Model Identification, Training and Control Alexandre P. Alves da Silva, Federal Engineering School at Itajuba, Brazil Chapter 5: Fuzzy Systems Applications to Power Systems Kevin Tomsovic, Washington State University Evolutionary Techniques and Fuzzy Logic in Power Systems Table of Contents Chapter 1: Theory of Evolutionary Computation .......................................................................................... 4 1.1 Introduction.......................................................................................................................................... 4 1.2 EC Paradigm Attributes ....................................................................................................................... 4 1.3 Implementation .................................................................................................................................... 4 1.4 Genetic Algorithms.............................................................................................................................. 5 1.4.1 Introduction................................................................................................................................... 5 1.4.2 An Overview of Genetic Algorithms ............................................................................................ 5 1.4.3 A Simple GA Example Problem................................................................................................... 6 1.4.4 A Review of GA Operations......................................................................................................... 8 1.5 Particle Swarm Optimization............................................................................................................. 11 1.5.1 Introduction................................................................................................................................. 11 1.5.2 Simulating Social Behavior ........................................................................................................ 12 1.5.3 The Particle Swarm Optimization Concept................................................................................. 13 1.5.4 Training a Multilayer Perceptron................................................................................................ 13 1.6 Conclusions........................................................................................................................................ 15 1.7 Acknowledgments.............................................................................................................................. 16 1.8 Selected Bibliography........................................................................................................................ 16 Chapter 2: An Introduction to Fuzzy Inference ............................................................................................ 19 2.1 Fuzzy Sets.......................................................................................................................................... 19 2.2 Differences Between Fuzzy Membership Functions and Probability Density Functions .................. 19 2.3 Fuzzy Logic ....................................................................................................................................... 21 2.3.1 Fuzzy If-Then Rules ................................................................................................................... 22 2.3.2 Numerical Interpretation of the Fuzzy Antecedent ..................................................................... 22 2.3.3 Matrix Descriptions of Fuzzy Rules ........................................................................................... 24 2.4 Application to Control ....................................................................................................................... 24 2.5 Variations........................................................................................................................................... 25 2.5.1 Alternate Fuzzy Logic................................................................................................................. 25 2.5.2 Defuzzification............................................................................................................................ 25 2.5.3 Weighting Consequents .............................................................................................................. 26 2.6 Further Reading ................................................................................................................................. 26 Chapter 3: Application of Evolutionary Technique to Power System Security Assessment ........................ 27 3.1 Abstract.............................................................................................................................................. 27 3.2 Introduction........................................................................................................................................ 27 3.3 NN's for DSA..................................................................................................................................... 28 3.4 Evolutionary-Based Query Learning Algorithm................................................................................28 3.5 Case Study – IEEE 17 Generator System .......................................................................................... 29 3.6 Conclusions........................................................................................................................................ 30 3.7 References.......................................................................................................................................... 30 Chapter 4: Application of EC to Optimization, Model Identification, Training and Control ....................... 32 4.1 Optimization ...................................................................................................................................... 32 4.1.1 Modern Heuristic Search Techniques .......................................................................................... 32 4.1.2 Power System Applications ........................................................................................................ 33 4.1.3 Example ...................................................................................................................................... 34 4.2 MODEL IDENTIFICATION ............................................................................................................ 34 4.2.1 Dynamic Load Modeling ............................................................................................................ 35 4.2.2 Short-Term Load Forecasting ..................................................................................................... 35 4.3 TRAINING ........................................................................................................................................ 36 4.3.1 Pruning Versus Growing............................................................................................................. 36 4.3.2 Types of Approximation Functions ............................................................................................ 37 4.3.3 The Polynomial Network............................................................................................................ 37 4.4 CONTROL......................................................................................................................................... 38 4.5 ACKNOWLEDGMENTS ................................................................................................................. 38 4.6 REFERENCES .................................................................................................................................. 38 Chapter 5: Fuzzy Systems Applications to Power Systems..........................................................................41 5.1 Introduction........................................................................................................................................ 41 5.2 Power System Applications ............................................................................................................... 42 5.2.1 Rule-based Fuzzy Systems.......................................................................................................... 42 5.2.2 Fuzzy Controllers........................................................................................................................ 43 5.2.3 Fuzzy Decision-Making and Optimization ................................................................................. 43 5.3 Basics of Fuzzy Mathematics ...........................................................................................................