1 Fuzzy Systems Applications to Power Systems K. Tomsovic School of Electrical Engineering and Computer Science Washington State University Pullman, WA 99164 tomsovic@eecs.wsu.edu Abstract: This chapter overviews the applications of fuzzy logic in power systems. Emphasis is placed on understanding the types of uncertainties in power system problems that are well-represented by fuzzy methods. Specific examples in the areas of diagnostics and controls are used to illustrate such concepts. Keywords: Distribution systems, fuzzy control, fuzzy numbers, fuzzy linear programming, preventive maintenance, reliability. 1 Introduction The purpose of this chapter of the short-course is to overview the relevance of fuzzy techniques to power system problems, to provide some specific example applications and to provide a brief survey of fuzzy set applications in power systems. Fuzzy mathematics is a broad field touching on nearly all traditional mathematical areas, the ideas presented in this discussion are intended to be representative of the more straightforward application of these techniques in power systems to date. Fuzzy logic technology has achieved impressive success in diverse engineering applications ranging from mass market consumer products to sophisticated decision and control problems [1, 2]. Applications within power systems are extensive with more than 100 archival publications in a 1995 survey [3]. Several of these applications have found their way into practice and fuzzy logic methods have become an important approach for practicing engineers to consider. Here, the focus is on the more general concepts. The reader is referred to [3,4] for a more detailed survey of the literature. Fuzzy sets were first proposed in the early 1960s by Zadeh [5] as a general model of uncertainty encountered in engineering systems. His approach emphasized modeling uncertainties that arise commonly in human thought processes. 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” [6]. Fuzzy sets began as a generalization of conventional set theory. Partially as result of this fact, fuzzy logic remained the purview of highly specialized technical journals for many years. This changed with the highly visible success of numerous control applications in the late 1980s. Although fuzzy mathematics arose and developed from the systems area, it perhaps belongs best to in the realm of Artificial Intelligence (AI) techniques as an interesting form of knowledge representation. Still, the primary development of fuzzy techniques has been outside the mainstream AI community. Uncertainty in fuzzy logic typically arises in the form of vagueness and/or conflicts, which are not represented naturally within the probabilistic framework. To be sure, uncertainty in reasoning may arise in a variety of ways. Consider the most common sort of discourse about a system among experts, and say to be more specific, a statement relevant to contaminants in the insulating oil of high voltage transformers The moisture level in the oil is high While this is a vague statement that does not indicate an exact measurement of the moisture, it does convey information. In fact, one might argue that this conveys more information than merely the actual moisture measurement since the qualifier “high” provides an assessment of the oil condition. Clearly, such a statement contains uncertainty, that is, the moisture level, the severity of the high reading, the implication of such moisture content, and so on, are all imprecise and may require clarification. Fuzzy sets emphasize the importance of modeling such uncertainty. With some effort, traditional probabilistic methods can be adapted to these problems. Still, researchers in the fuzzy set area have found that this is not usually an effective approach. To begin, the fuzzy set approach poses new views of systems that has resulted in such novel applications as fuzzy logic control. More importantly, fuzzy sets create a framework for modeling that does not exist under probability. Less formal methods, such as, certainty factors do not allow for as systematic as an approach. Still, there remains controversy among researchers about the need for fuzzy mathematics and a variety of techniques have arisen in both the Systems and Control community and the AI community to address similar problems. This paper will sidestep such controversy but it is worth noting the large number of successful applications of fuzzy logic and while subsequent developments may lead to