A NLP-MILP iterating algorithm for operational planning in electrical distribution systems

We consider a class of optimal power flow (OPF) applications where some loads offer a modulation service in exchange for an activation fee. These applications can be modeled as multi-period formulations of the OPF with discrete variables that define mixed-integer non-convex mathematical programs. We focus on the optimization of this Mixed-Integer Non-Linear Programming (MINLP) problem through a separation into a non-linear programming (NLP) and a mixed-integer programming (MIP) component. The NLP is a feasibility problem involving the power flow equations and the flexible loads needs. The MIP is used to choose which flexible loads to activate and in which order. In several papers, the MIP is based on a linearization of the non-linear power flow equations. We compare several variants of the linearization. We propose new formulations based on prior knowledge of the network to improve the decision-making process when the relaxation is inappropriate. We show computationally with many real-world instances that they help find feasible solutions faster than standard MINLP techniques.