Fuzzy Graph-Theoretic Reliability and Fault Tolerance in Electrical Networks

Abstract

Reliability and fault tolerance represent important factors that should be considered in the process of designing and studying electrical networks. Graph-theoretic approaches allow one to describe network elements as vertices and their connections as edges. In case if there is some level of uncertainty in relation to the conditions of components and connections between them, there may be a need in a more flexible approach to modelling. Fuzzy graph theory represents an approach where this uncertainty can be expressed using membership values of vertices and edges. This paper aims at developing a model based on fuzzy graph theory that would be used to investigate structural reliability and fault tolerance of electrical networks. It will take into account fuzzy connectivity, path strength, critical elements and structural transformations due to the deletion of vertices and edges. Mathematical statements and theorems would be suggested to analyze the relations between these concepts and maintaining of network connectivity after element failures. Several examples of hypothetical electrical networks would be used to illustrate the proposed concepts and compare different network structures. The research is focused on the analysis of structural reliability in the context of fuzzy models and it does not consider failure probability and real electrical characteristics.