A graph-based direct approach for distribution systems with PV nodes

This paper presents a graph-based direct approach for distribution systems with PV nodes. The contribution of this paper mainly includes two points: First, without building the bus-injection to branch-current (BIBC) matrix and the branch-current to bus-voltage (BCBV) matrix, we based on graph theory develop an uniformed formulation between bus current injections and bus voltages for both radial and meshed networks, so that extra processing for meshed network such as breaking meshes and loop analysis are not required; second, instead of secant method or sensitivity matrix method, we present an efficient method for handling PV nodes based on feedback control, which regarding PV nodes as PQ nodes and regulating reactive power of PV nodes by the mismatch of voltage magnitude. Besides, the convergence of the proposed method is proved by using the Banach fixed-point theorem.