Efficient Graph Theory Based Load Flow Solver for DC Distribution Networks Considering DC/DC Converter Models

This paper proposes a load flow (LF) solver for DC distribution networks by incorporating generic DC/DC converter models for buck, boost, and buck-boost operations. A generic LF solver is formulated using the developed DC/DC converter models by taking advantage of graph theory for DC grids. The proposed method is based on Laplacian Matrix (LM) formulation. Due to non-linearities induced by constant power terminals (CPTs) and distributed generators (DGs), the proposed formulation will be solved iteratively. Instead of using classical bus power injections, the summation of line flows is employed in LF calculation to account for connections to buses with different converter operations. The main advantage of this formulation is that the Laplacian Matrix for a given DC network needs to form only once before starting the iterative procedure, and it will remain constant throughout the process. The proposed method utilizes an improved LM technique, so it has no topology constraints. To validate the proposed method, the modified IEEE 33 bus test feeder is simulated in MATLAB with different configurations and loading conditions. The accuracy of the proposed method is validated by comparing the results with Electromagnetic Transient (EMT) simulations. The results show that the proposed method can handle all DC/DC converter operations and can provide a fast LF solution for DC distribution networks.