An iterative method of constant slope for solution of nonlinear equations in electrical power systems

In this paper, a constant slope method is applied to solve nonlinear equations and calculate the Voltage and load flow in an electrical power system. In an electrical power system of N nodes, N-1 non-linear equations are established, and they are related; the power in each node, the admittance matrix and the nodal Voltage. These equations are solved with an iterative method of slope constant of five steps. The theoretical foundations of the method and convergence analysis it's included in the paper. The method is applied to different test systems and the results obtained show differences in the magnitude of the Voltage, ranging from 0.05% to 5.0%. Due to the formulation, the number of iterations is high, however, since only elementary algebraic operations are carried out, the execution time ranges between 16 and 180 milliseconds.