Mathematical theory of electrical networks.

Abstract

In this thesis an attempt has been made to present a mathematical model of an electrical network based on Kron's work and further to use this model, for analyzing electrical network problems. To begin with, we shall represent an electrical network as a linear graph. The electrical network problem is presented in an abstract topological form, and the condition on the property of branch impedance matrix for the unique existence of the solution is developed. The various contradictions of the linear graph model are then pointed out. To remove these contradictions, a topological model, consisting of branches only, which is called the branch network or 1-network by Kron is introduced. The various concepts of 1-networks are generalized to any dimension p. The properties of p-networks are described with the help of elementary concepts of algebraic topology. Finally, diakoptic and co-diakoptic property of p-network is described as a direct outcome of p-network theory.