Abstract The power flow in electrical system permits analyzing and studying the steady-state behavior of any grid. Additionally, the power flow helps with the proper planning and management of the system. Therefore, it is increasingly necessary to propose power flows with fast convergence and high efficiency in their results. For this reason, this paper presents an alternative power flow approach for direct current networks with constant power loads based on a truncated Taylor-based approximation. This approach is based on a first-order linear approximation reformulated as a recursive, iterative method. It works with a slope variable concept based on derivatives, which allow few iterations and low processing times. Numerical simulations permit identifying the best power flow approaches reported in the specialized literature for radial and mesh dc grids, including the proposed approach. All the simulations were conducted in MATLAB 2015 a .