Power harmonics pattern recognition by solving fuzzy equations

The aim of this paper is to introduce an approach to solve equations involving fuzzy numbers by optimisation. The technique is illustrated by an application in power system harmonics pattern recognition. Subject to the intrinsic uncertainty associated with the harmonics spectrum of different loads of the same type and the errors of the measuring equipment, fuzzy approach becomes a necessity to handle such a problem. A method to identify the patterns of harmonics distribution of each type of common customer load by fuzzy numbers is described. A set of linear equations involving fuzzy constants and crisp variables is formulated for an electric power system. Furthermore, power system harmonics pattern recognition by cost function optimisation is presented as a solution to the set of linear equations. Such analysis leads to the definition of a fuzzy logic based indicator that can truly reveal the degree of seriousness of harmonics pollution at any utilisation point of electric power. The methodology described in this paper can be extended to similar problems in other areas.