Comparison of the fuzzy regression analysis and the least squares regression method to the electrical load estimation

An essential point in correct calculations and analysis of power distribution systems is a proper evaluation of loads. The acquisition of this data is complex because of a large number of nodes and their area distribution. As a rule receiving nodes are not equipped with stationary measuring instruments so measurements of loads are performed only sporadically. The theory which enables efficient description of unreliable and inaccurate data, and relationship between them, is the fuzzy set theory. The paper presents possibilities of application of the fuzzy set theory to power distribution system calculations. Unreliable and inaccurate input data were modeling by means of fuzzy numbers. A regression model, expressing the correlation between a substation peak load and a set of customer features (explanatory variables), existing in the substation population, is determined. The fuzzy set approach and standard regression method are compared.