An evaluation of an accuracy of the fuzzy regression analysis in the electrical load estimation

In a distribution system, bus load estimation is complicated because system load is usually monitored at only a few points. As a rule receiving nodes are not equipped with stationary measuring instruments so measurements of loads are performed sporadically. In general, the only information commonly available regarding loads, other than major distribution substations and equipment installations, is billing cycle customer kWh consumption. In order to model system uncertainty, inexactness, and the random nature of customers´ demand, a fuzzy system approach is proposed. The paper presents possibilities of application of fuzzy set theory to electrical load estimation and the effect of different factors on the result of calculations. Unreliable and inaccurate input data have been modeled 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. Simulation studies have been performed to demonstrate the efficiency of the proposed scheme and an effect of different parameters on its accuracy on the basis of actual data obtained at distribution system substations.