Analytical model and algorithm for tracing active power flow based on extended incidence matrix

This paper proposes an analytical model and algorithm for tracing power flow (TPF). The concept, construction approach and properties of extended incidence matrix (EIM) are developed. By using results of an AC or DC power flow solution from any off-line program or state estimation, the extended incidence matrix, generation and load power vectors, and distribution factor matrix are derived so that the analytical model of power transfers between generators and loads can be built. The major advantage of the proposed method is that the matrix theory is used to directly build the TPF model and no proportional sharing assumption on the flow distribution is needed. The method was tested using a 4-bus system, and the IEEE 30-bus and IEEE 14-bus power systems. The case studies indicate that the developed technique can be applied to any power system with or without loop flows.