Power flow solution in direct current grids using the linear conjugate gradient approach

The Colombian power system is being modified by the large-scale integration of renewable energy resources and energy storage systems, in conjunction with the microgrid concept that originates the possibility of alternating and direct current grids or hybrid between them. Here, we propose a classical gradient conjugate method to solve linear algebraic equations without matrix inversions, to address the power flow problem in electrical direct current networks with constant power loads, to contribute with the paradigm of microgrids operated in direct current. This methodology can be applied to the power flow equations since the admittance matrix is positive definite and diagonal dominant which guarantees convergence of the power flow problems. Numerical simulations evidence the applicability of the gradient conjugate method to solve power flow problems in direct current networks with radial and mesh topologies. All the simulations are conducted in MATLAB software version 2017a licensed by the Universidad Tecnológica de Bolivar, Colombia.