Research on relation between two approaches of power flow tracing

There are two main algorithms for power flow tracing,one is based on the solution of simultaneous linear equations,the other is based on the graph theory.In this paper,the upstream and downstream tracing distribution matrices are researched in the form of matrix power series in order to prove the relation between the two approaches.It proves not only the realtion between the two approaches in mathematics,but also provides an additional insight into the tracing methodology.The example with a 4-bus system is given to demonstrate the accuracy of the proposed conclusion.