Topological properties of sequential network analysis

Abstract

Sequential network analysis is a method of analyzing a network by choosing some independent variables among the unknown variables in the network, expressing the remaining unknown variables sequentially in terms of the independent variable by applying KCL and KVL, and then solving the constraint equations obtained as the result of the sequential process to determine the independent variables. This paper deals with the topological properties of a sequential analysis formulated f o r an active network. represented by current-and voltage-graphs. The set of edges whose unknown variables are chosen as independent variables is called the independent-edge set (denoted by Ed, the set of edges at which the constraint equations are obtained is called the constraint-edge set (denoted by Eu), and the set of edges whose unknown variables are expressed in terms of the independent variables is called the covered-edge set (denoted by Ep ) .The sequential step of the analysis proceeds by repeatedly adding to EP a n edge which is currentdependent and/or voltage-dependent with respect to EP. Thus a sequence of covered-edge sets is obtained. The conditions for current-dependent, voltage-dependent, independent and constraint edges are presented and the duality among them is also clarified. From the sequence of ED a sequence of Ep U Eb -EU is obtained. Each of the sets in this sequence specifies the electrical connectivities between Eb and Eu. The relation between the edge sets defined above and the structure of 2-graphs is given. Finally, minimum independent-edge sets are given for some special types of graphs, and an algorithm to decrease the number of independent edges is presented.?he network topology is