On current trace problem

Abstract

The pricing of electricity trasmission requires determining how much use each generator is making of a transmission line and what is each generator’s contribution to the system losses. Such problems cannot be solved by only using Kirchoff’s laws. This paper proposes two current decomposition axioms based on which the theories and models are established for the current trace problem. To create an efficient algorithm the graph theory is employed. It is proved that there is no directed circuit in a directed current distribution graph. According to this theorem a very simple and efficient algorithm based on recursive elimination process is suggested. A simple example is used to explain the algorithm.