Graph-theoretic based approach for the loadflow solution of three-phase distribution network in the presence of distributed generations

Abstract

Matrix is one of the convenient means for depicting/illustrating a graph on the computer. In this study, the notiongraph-theory in conjunction with matrix algebraic operations has been adopted for solving the load-flow problem of three-phasedistribution systems (radial and meshed). Five significant matrices, path impedance (PI), loads beyond branch (LB), path drop(PD), slack bus to other buses drop (SBOBD), load flow matrix (LFM), and straight-forward matrix operations have been utilisedto attain the load-flow solutions. The aforementioned matrices reveal the system's topology and pertinent information about theoperating characteristics of the distribution system during LF studies. This algorithm is formulated entirely on various matricesformulation and computations, even at the stage of upgrading the voltage at every individual bus. Owing to the aforementionedreasons, this LF methodology is computationally efficient for large-sized distribution systems. Moreover, the distributedgenerations (DGs) modelled as PQ and PV buses are incorporated into the proposed load-flow algorithm. A generalisedbreakpoint matrix has been derived to compute the mesh breakpoint and PV breakpoint injections simultaneously. Theeffectiveness of the proposed methodology has been tested on several standard distribution systems. The test outcome showsthe viability and accuracy of the proposed method.