Minimal cut sets, Petri nets, and prime number encoding in distribution system reliability evaluation

Reliability assessment of secondary distribution networks is an important subject due to the increasing demand for more reliable service with less interruption frequency and duration. The connection of a distribution network may be neither series nor parallel, and analyzing such a network is a complicated process and time consuming task. In this paper, a technical approach for evaluating the reliability of a mesh networked distribution system is described. The proposed method is based on the identification of circuit minimal tie sets using the concept of Petri nets. Then, prime numbers encoding and unique prime factorization are applied to classify the remaining combinations as tie sets, cut sets, or minimal cut sets. The minimal cut sets are used to calculate the Availability (A), Average Interruption Frequency (AIF), and Average Interruption Duration (AID) of the network. Examples are shown to illustrate the proposed method. The method shown is algorithmic and appears suitable for off-line comparison of alternative secondary distribution system designs on the basis of their reliability.