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