Graph Based Power Flow Algorithm for Single Phase Radial and Weakly Meshed Distribution System in the presence of Distributed Generations

This work focuses on proposing a graph theory-based power flow (PF) solution for distributed energy resources (DERs) integrated single-phase radial and weakly meshed distribution networks. Several Matrices have been formulated which have been further classified into two categories. The first category of the matrix depicts the configuration and topology of the network, and the second one is deployed for the computation of PF parameters utilizing the property of the first one. The PF problem of distribution networks requires unique treatments to deal with weakly meshed configurations, and multiple DGs modeled as PV buses. For such a scenario, a compensating matrix has been formulated to calculate the pertinent additional current to be injected to compensate for the voltage magnitude difference between the two ends of each mesh break-point, and/or between computed and specified values at the PV bus. This computed current needs to be injected into the respective mesh breakpoints, and/or into the respective PV bus present in the network. The calculated pertinent injections are contemplated in the net branch current matrix. This helps in solving the PF problem of the network with weakly meshed structures, and DERs in a similar fashion to the radial network problem. Pertinent tests have been completed to examine the convergence nature and computational ability of the proposed PF technique.