Graph-Based Power Flow Algorithm for Three-Phase Distribution Network Considering Regulators and Distributed Generations

In this article, a new approach for solving the power flow (PF) problem of distributed generations (DGs) integrated three-phase distribution networks is proposed that is based on backward-forward sweep, graph theory, and matrix algebra. The key concept is the formation of two matrices, one that depicts the configuration or structure of the distribution system (these matrices are connectivity matrix and bus-branch topology matrix) and the second which is directly involved in computing PF parameters. The major advantage of the architecture is that the size of matrices and sparsity problems can be handled better than contemporary approaches making the approach very robust and efficient. To emulate the feature of DGs modeled as PV bus into the proposed power flow algorithm, a PV injection sensitivity matrix has been developed which facilitates computation of the required reactive power injections to offset the voltage deviation at PV bus. The computed injection is replicated in the PF using PV current beyond the branch matrix and net branch current matrix. Several test analyses have been carried out to validate the viability and efficiency of the proposed PF algorithm.