Algebraic Model of Electrical Network

Abstract

The set of all possible electrical states of a network is modeled using linear algebra and group theory. The model which is the multidimensional linear space is established, described, and verified. The formulas are derived making possible numerical calculations and network analysis. All possible methods of network solution are modeled and discussed using linear transformation theory. The degree of freedom of a network is defined and described. Finally, the classification of networks is proposed as far as topological structures and methods of solution are concerned. The theory developed makes possible a more general approach and solution to power system problems.