Dynamic mixed integer nonlinear programming applied to the resolution of the optimal power flow problem incorporating the definition of sequences of control adjustments

Abstract

Although Optimal Power Flow (OPF) formulations in the correlate literature focus on "solely" determining the optimal adjustments of power system controls, defining a sequence of control adjustments is a critical task for the practical use of OPFs in real-time optimal operation of power systems, as all control adjustments must be coordinated whilst the current operation point smoothly moves toward the optimum. Many approaches in the literature deploy local differential sensitivity analysis to define such sequence of control adjustments, however, such techniques are only effective in a neighborhood around the current operating point given the nonlinear and non convex characteristic of OPF formulations. In this context, the objective of this research project is to solve the OPF problem incorporating the definition of a sequence of control adjustments (more specifically, the optimal reactive dispatch problem for the minimization of active power losses in transmission power systems), whose formulation is methodologically founded on Mixed-Integer Dynamic Nonlinear Programming (MIDNLP) problems. For this, a review on the literature will explicit the concepts associated with resolution techniques of MIDNLP problems and continuous relaxation techniques of binary variables by penalty and/or sigmoidal functions that transform the original problem into a Nonlinear Programming (NLP) problem. The model proposed in this research project will be implemented in the AMPL environment for mathematical programming and its resolution will be carried out by commercial solvers. Numerical results for IEEE test-systems and realistic power systems whose data are available in the correlate literature will be used to validate the proposed resolution approach. (AU)