The fuzzy regression approach to peak load estimation in power distribution systems

This paper presents a new scheme based on the fuzzy regression analysis for the estimation of peak load in distribution systems. In distribution systems, bus load estimation is complicated because the 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 random nature of customers' demand, a fuzzy system approach is proposed. This paper presents possibilities of application of the fuzzy set theory to power distribution system calculations. Unreliable and inaccurate input data have been modeled by means of fuzzy numbers. Trapezoidal and triangular forms of fuzzy numbers were used for description of input data. 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 on the basis of actual data obtained at two distribution system substations. The same data have been used for building standard linear regression models. Comparison of the performance of both methods has been done.