A Modified Barrier and Barrier Method and the Optimal Power Flow Problem

Abstract

This work proposes an approach that uses a union of methods based on logarithmic barrier function and modified logarithmic barrier function for the resolution of the reactive optimal power flow problem. In this proposed approach the inequality constraints are transformed into equalities by adding the slack variables, which are handled by logarithmic barrier function or modified logarithmic barrier function, and the equality constraints are handled by means of Lagrange multipliers. These methods are used in two steps. Initially, the method based on the logarithmic barrier function is applied until the transition condition is satisfied. After the method based on modified logarithmic barrier function is used until the stop condition is satisfied. Numerical tests carried out with the IEEE 14, 30, 57 and 118 bus electrical systems indicate that the proposed approach is efficient in the resolution of the reactive optimal power flow problem and the results obtained by the proposed approach were compared with the logarithmic barrier method and the logarithmic barrier method modified, separately.