A Graph-Based Power Flow Method for Balanced Distribution Systems

A power flow method based on graph theory is presented for three-phase balanced distribution systems. The graph theory is used to describe the power network and facilitate the derivation of the relationship between bus Currents and the bus Voltage Bias from the feeder bus (the CVB equation). A distinctive feature of the CVB equation is its unified form for both radial and meshed networks. The method requires neither a tricky numbering and layering of nodes nor breaking meshes and loop-analysis, which are both necessary in previous works for meshed networks. The convergence of the proposed method is proven using the Banach fixed-point theorem.