In this paper, an iterative Newton-type method of three steps and fourth order is applied to solve the nonlinear equations that model the load flow in electric power systems. With the proposed method (N-1) non-linear equations are formulated and solved iteratively to calculate the Voltage in each node of an electrical system. The justification of the method and its theoretical preliminaries are presented in this paper. The proposed method is applied to IEEE test systems, and their results are compared obtaining a maximum error of 0.5%. From the results obtained, the proposed method is an alternative to solve load flows in electrical systems.

This paper was developed with the purpose of knowing the behavior of radial distribution systems that operate in balanced conditions. Two algorithms were used to calculate the voltage at the network nodes and with them the load flow in each line. With the application of Kirchhoff's laws of electrical circuits, a one-dimensional arrangement of order N and a two-dimensional arrangement of order Nx5 are generated, both depend on the impedances and the shunt admittances. With these two arrangements, a non-linear function f (V1, V2 ,,, VN,, Sc) was generated, which depends on the voltages Vi and the complex power Sc demanded at each node of the distribution system. These equations were solved iteratively, two methods were applied; In the first method, the Halley formula with an acceleration factor α was used to solve the non-linear function f (V1, V2 ,,, VN,, Sc), in the second method, the Gaussian method was applied in the same way that it is used for load flows in interconnected systems. The two algorithms were applied to test systems of 40, 70 and 80 nodes, obtaining results similar to those reported in the specialized literature where they make use of other solution methods. In the author's opinion, the proposed algorithms represent alternatives for the study of energy distribution systems. An advantage of the methods is that they are simple code and there are differences between them, the second method has a faster convergence.