Two Iterative Methods to Solve Nonlinear Equations of Load Flows

Abstract

This paper presents the results obtained when two iterative methods are applied to the solution of non-linear equations that model the load flow in electric power systems. Two iterative methods are applied; the first consists of a simplification of the rectangular form the traditional Newton-Raphson method, the second is a hybrid method and relates the simplified form proposed here and a four-step Newton-type iterative method. The convergence characteristic and the mathematical preliminaries of the iterative four-step method are included in the paper. The methods were used to calculate the voltages at each node of the IEEE test system of 118 nodes and a distribution system of 40 nodes. In each method, the formation of the Jacobian matrix, widely used in traditional forms of load flows, is avoided and only elementary operations are carried out, impacting the execution times for the test systems used, being of the order of 15.6 to 279 milliseconds. The maximum error found is for the 118 node system and is of the order of 3.7%.