Outer Approximation Method for Discrete AC Optimal Power Flow

This paper introduces an Outer Approximation (OA) method for solving discrete AC Optimal Power Flow (OPF) problems that account for switching decisions. The OPF problem is formulated via the extended conic quadratic format. It includes selecting generators for dispatch and controlling switched-type capacitor/inductor banks. The OA method is based on relaxing nonlinear equality constraints into conic and linear inequalities with penalty slack variables. The resulting Mixed-Integer Second-Order Cone Programming (MISOCP) solution is iterated with a continuous variable Nonlinear Programming (NLP) solver that holds the discrete decisions constant at their most recent MISOCP values. The OA method can utilize polyhedral approximations and is scalable to test instances with more than 3000 nodes. Comparisons are reported with globally optimal discrete AC OPF results from the recent literature and a commercial solver for nonconvex Mixed-Integer Nonlinear Programming (MINLP) utilizing dynamic outer approximation and piecewise linear approximation with spatial branching. Comparative analysis shows that the proposed OA method provides global solutions for previously studied test instances while offering significant speed-up. It also applies to larger test networks where the other methods fail to calculate a feasible solution.