A Proposed Methodology Involving Progressive Bounded Constraints And Interior-Exterior Methods in Smoothed Economic/Environmental Dispatch Problems

Abstract

This paper proposes a methodology involving the primal-dual predictor-corrector interior/exterior point, the progressive bounded constraints and the arctangent smoothing methods, to be applied in economic/environmental dispatch multi-objective problem with valve-point load effects. The interior/exterior point method explores the logarithmic barrier modified function, which belongs to the nonlinear rescaling methods, allowing it a relaxation of the feasible set that includes its boundary, to iterate with exterior and unfeasible points. To treat non-convex functions, the inertia correction strategy is considered to ensure that it produces descent directions, avoiding the convergence to stationary points which are not local minima. Besides, the arctangent smoothing technique is used to treat nonsmooth functions and their modular parts, which are the main characteristic of the economic dispatch function. The progressive bounded constraints method are used to transform the multi-objective problem into a set of mono-objective subproblems and to allow that the economic/environmental dispatch multi-objective problem was solved by the proposed methodology, which was applied to solve test problem with nineteen and forty generating units. The results are compared with others published in the literature and with the solver Knitro.