Assessment of Equipment Trip Probability Due to Voltage Sags Based on Fuzzy Possibility Distribution Function

Assessment of equipment trip is needed for proper estimation of interruption/disruption cost and voltage sag mitigation. The equipment trip depends on the severity of voltage sag and the tolerance of the equipment toward the sag. However, the occurrence of voltage tolerance of an equipment in between the two known bound levels is uncertain in nature. The existing evaluation methods for equipment trip analysis fail to properly assess this uncertain property of voltage tolerance curves. This paper presents a novel approach to assess the equipment trip by handling the uncertainties by using fuzzy probability and possibility distribution. A new method is proposed to transform a rigorously performed statistical data into a fuzzy possibility distribution function, which eliminates the ambiguity that comes with the non-standardized selection of membership function/possibility function. With the proposed method, the statistical data are used to extract the fuzzy probability distribution of voltage sag intensity, which is given by both the magnitude and time duration of voltage sags, while the concept of fuzzy probability is used to calculate the fuzzy trip probability or equipment failure probability. The proposed method is finally applied to estimate the number of trips for six different sensitive equipments connected to two practical Indian distribution systems.