The analysis method of the sets of branches based on independent loops in the electric network

Abstract

The matrixD describing relations of the loops to the nodes in the graph and also the sets of branches based on the independent loops and their matrixQ are defined. The theorem in which the product of the loop-node matrixD multiplied by the incidence matrixA _a is equial to matrixQ is put forward and proved. The admittance matrixY _lc of the sets of the branches is defined and it is assumed that the vectorV _lc of voltage of the sets of branches to be a calculative quantity. The equation of the sets of branches is derived and the analysis method of the sets of branches based on the independent loops in the electric network is presented.