An Exact Sequential Linear Programming Algorithm for the Optimal Power Flow Problem

Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is largely due to LP technology's superior reliability and computational efficiency, especially in real-time market applications, security-constrained applications, and extensions involving integer variables, in addition to its ability to readily generate locational marginal prices (LMP) for market applications. In the aim of leveraging the advantages of LP while retaining the accuracy of NLP interior-point methods (IPMs), this paper proposes a sequential linear programming (SLP) approach consisting of a sequence of carefully constructed supporting hyperplanes and halfspaces. The algorithm is numerically demonstrated to converge on 138 test cases with up the 3375 buses to feasible high-quality solutions (i) without AC feasibility restoration (i.e., using LP solvers exclusively), (ii) in computation times generally within the same order of magnitude as those from a state-of-the-art NLP solver, and (iii) with robustness against the choice of starting point. In particular, the (relative) optimality gaps and the mean constraint violations are on average around $10^{-3}$% and $10^{-7}$, respectively, under a single parameter setting for all the 138 test cases. To the best of our knowledge, the proposed SLP approach is the first to use LP exclusively to reach feasible and high-quality solutions to the nonconvex AC OPF in a reliable way, which paves the way for system and market operators to keep using their LP solvers but now with the ability to accurately capture transmission losses, price reactive power (Q-LMP), and obtain more accurate LMP.