Distribution transformer load modeling with interval Type-2 Fuzzy Sets

In this paper we present a novel way of modeling the transformer load variation using Fuzzy Sets. A standard rural distribution transformer load variation that is uncertain over a period of 24-hour duration is modeled as fuzzy trapezoidal membership functions (Type-1). Here we have considered a rural distribution feeder as our test system, for which total kVA duration curves are measured for each day of a month, from which the kVA loading at each node is obtained based on the kVA ratings of the respective transformers at that nodes. The total one month trapezoidal membership functions (Type-1 trapezoidal membership functions for a single day) together are represented as Interval Type-2 Trapezoidal membership function, so that the uncertainties in the load variations at the transformer are taken into consideration. The proposed transformer load modeling and measures of uncertainty of type-2 fuzzy set helps the system planner to study the distribution system voltage profile, power losses and power flow variations under uncertain load variation conditions.