## A Decoupled Method for Solving Distribution Networks with PV Nodes

**Authors:**Augugliaro, A; Dusonchet, L; Favuzza, S; Ippolito, MG; Riva Sanseverino, E**Publication year:**2009**Type:**Articolo in rivista (Articolo in rivista)**Key words:**Backward/forward method, Distribution Networks, Power Flows**OA Link:**http://hdl.handle.net/10447/43205

### Abstract

In this paper, a methodology for the load flow solution of distribution systems with fixed voltage nodes (PV nodes) is presented. The proposed technique is the extension of a methodology already set up by the authors to solve distribution systems; it is an iterative approach devoted to the treatment of voltage dependent loads; at each iteration, all the network components (lines, loads, and PV nodes) are represented by resistances and reactances. The methodology is based on the identification of two networks that are solved in sequence, thus allowing the attainment of state features of the original system. One of the two systems is made up only of shunt and series resistances; the other only of shunt and series reactances. If the network is meshed, it is made radial by means of cuts and the injection of currents in the nodes created by the cuts. The unknown features are: the shunt currents in the terminal nodes of the radial or radialized system; the currents injected in the cut nodes of the meshes; and the currents injected in the shunt reactances of the PV nodes. In each of the two systems, all the unknown currents are attained by the solution of a linear system of equations in which all the coefficients of the unknowns and the known terms are deduced, with a backward process, at the branching points of the meshes, at the PV nodes, and at the source node. In the paper, after having recalled the state of the art in the backward/forward methods that are now the most commonly used for distribution systems, the methodology set up by the authors is summarized. Then the PV bus model is illustrated as well as the methodologies for the construction of the matrix of the coefficients of the unknowns and for the construction of the known terms array. Finally, the results of some applications that aim at verifying the speed of convergence and the precision of results are reported.