Learning Interior Point Method for AC and DC Optimal Power Flow

Abstract: This paper proposes a feasibility-guaranteed learning interior point method (L-IPM) to solve both AC and DC optimal power flow (OPF) problems. Given the criticality of OPF, the proposed L-IPM uses a hybrid learning model approach rather than relying solely on a simple black-box prediction. The traditional IPM follows a central path from an initial point to the optimal solution. However, each iteration involves solving large linear systems, which becomes increasingly expensive as the matrices grow more ill-conditioned in later steps. To address this, we model the IPM trajectory as a time series and train a Long Short-Term Memory (LSTM) network to project the IPM central path using only the first few stable iterations, which carry the most informative features about the path to optimality. We introduce a grid-informed methodology that enforces operational constraints on generation, voltage magnitudes, and line flows to ensure feasibility. The grid-informed LSTM serves as a tool for the IPM central path projection and, followed by a final IPM refinement step, significantly reduces the total number of iterations and time required for convergence. We use a sampling method to generate a wide range of load scenarios to improve generalization across diverse operating conditions, efficiently covering the power system's operational space. Simulation results on a 2869-bus European high-voltage transmission system show that the proposed L-IPM significantly reduces solution time by up to 94\%, while maintaining accuracy and feasibility of the solution. By leveraging early iterations and bypassing the final ill-conditioned and computationally demanding steps of traditional IPM, the proposed L-IPM reduces the number of required iterations by up to 85.5\%. Since solution feasibility is also guaranteed, L-IPM outperforms the conventional IPM in both computational efficiency and robustness.