On the Existence of the Power Flow Solution in DC Grids With CPLs Through a Graph-Based Method

This brief explores the formulation of the power flow problem in DC grids with a classical incidence matrix through a graph-based formulation. This corresponds to a compact representation of the conventional backward/forward sweep methods, which is applicable to radial and mesh networks with a unique voltage controlled source. To guarantee the existence and uniqueness of the power flow solution in the DC network under well-defined operative conditions, the Banach fixed-point theorem is employed. Simulation results confirm that the solution of the proposed method is numerically comparable with classical approaches, such as Gauss-Seidel, Newton-Raphson, successive approximations and Taylor-based methods. All the simulations are conducted in MATLAB software.