Upper-triangular matrix, branch-to-node incidence matrix, power flow methods, equivalent formulation, Technology, Engineering (General). Civil engineering (General), TA1-2040

This paper demonstrates that graph-based power flow methods for strictly radial distribution networks (one based on the upper-triangular matrix and the other on the incidence matrix or classical backward/forward power flow method) are equivalent, implying that both recursive power flow formulas are the same. A small distribution network composed of seven nodes and six distribution lines is considered to demonstrate this equivalence. The main contribution of this research lies in the fact that it obtains a matrix relation between the upper triangular matrix and the demand-to-demand branch-to-node incidence matrix. Numerical comparisons in single-phase distribution networks comprising 33, 34, 69, and 85 nodes and three-phase asymmetric networks comprising 8, 25, and 37 nodes confirm the theoretical results.