The alternating current optimal transmission switching (ACOTS) problem incorporates line switching decisions into the alternating current optimal power flow framework, offering well-known benefits in reducing operational costs and enhancing system reliability. ACOTS optimization models contain discrete variables and nonlinear, nonconvex constraints, which make them difficult to solve. In this work, we develop strengthened quadratic convex (QC) relaxations for ACOTS, in which we tighten the relaxation with several new valid inequalities, including a novel kind of on/off cycle–based polynomial constraints by taking advantage of the network structure. We linearize the sum of on/off trilinear terms in the relaxation using extreme-point representation, demonstrating theoretical tightness, and efficiently incorporate on/off cycle–based polynomial constraints through disjunctive programming–based cutting planes. Combined with an optimization-based bound-tightening algorithm, this results in the tightest QC-based ACOTS relaxation to date. We additionally propose a novel maximum spanning tree–based heuristic to improve the computational performance by fixing certain lines to be switched on. Our extensive numerical experiments on medium-scale power grid library instances show significant improvements on relaxation bounds, whereas tests on large-scale instances with up to 2,312 buses demonstrate substantial performance gains. To our knowledge, this is the first ACOTS relaxation-based approach to demonstrate near-optimal switching solutions on realistic large-scale power grid instances. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: The authors gratefully acknowledge support from the U.S. Department of Energy through Los Alamos National Laboratory’s directed research and development program [Grant 20230091ER: Learning to Accelerate Global Solutions for Non-Convex Optimization]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0236 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0236 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Contingency research to find optimal operations and postcontingency recovery plans in distribution networks has gained major attention in recent years. To this end, we consider a multiperiod optimal power flow problem in distribution networks, subject to the N – 1 contingency in which a line or distributed energy resource fails. The contingency can be modeled as a stochastic disruption, an event with random magnitude and timing. Assuming a specific recovery time, we formulate a multistage stochastic convex program and develop a decomposition algorithm based on stochastic dual dynamic programming. Realistic modeling features, such as linearized AC power flow physics, engineering limits, and battery devices with realistic efficiency curves, are incorporated. We present extensive computational tests to show the efficiency of our decomposition algorithm and out-of-samplex performance of our solution compared with its deterministic counterpart. Operational insights on battery utilization, component hardening, and length of recovery phase are obtained by performing analyses from stochastic disruption-aware solutions. Summary of Contribution: Stochastic disruptions are random in time and can significantly alter the operating status of a distribution power network. Most of the previous research focuses on the magnitude aspect with a fixed set of time points in which randomness is observed. Our paper provides a novel multistage stochastic programming model for stochastic disruptions, considering both the uncertainty in timing and magnitude. We propose a computationally efficient cutting-plane method to solve this large-scale model and prove the theoretical convergence of such a decomposition algorithm. We present computational results to substantiate and demonstrate the theoretical convergence and provide operational insights into how making infrastructure investments can hedge against stochastic disruptions via sensitivity analyses.

Distributed generation and remotely controlled switches have emerged as important technologies to improve the resiliency of distribution grids against extreme weather-related disturbances. Therefore it becomes important to study how best to place them on the grid in order to meet a resiliency criteria, while minimizing costs and capturing their dependencies on the associated communication systems that sustain their distributed operations. This paper introduces the Optimal Resilient Design Problem for Distribution and Communication Systems (ORDPDC) to address this need. The ORDPDC is formulated as a two-stage stochastic mixed-integer program that captures the physical laws of distribution systems, the communication connectivity of the smart grid components, and a set of scenarios that specifies which components are affected by potential disasters. The paper proposes an exact branch-and-price algorithm for the ORDPDC that features a strong lower bound and a variety of acceleration schemes to address degeneracy. The ORDPDC model and branch-and-price algorithm were evaluated on a variety of test cases with varying disaster intensities and network topologies. The results demonstrate the significant impact of the network topologies on the expansion plans and costs, as well as the computational benefits of the proposed approach.

This article considers a probabilistic generalization of the N‐k failure‐identification problem in power transmission networks, where the probability of failure of each component in the network is known a priori and the goal of the problem is to find a set of k components that maximizes disruption to the system loads weighted by the probability of simultaneous failure of the k components. The resulting problem is formulated as a bilevel mixed‐integer nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cutting‐plane algorithm is proposed to solve the convex relaxation and linear approximations of the N‐k problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small‐, medium‐, and large‐scale test instances; the test instances include the IEEE 14‐bus system, the IEEE single‐area and three‐area RTS96 systems, the IEEE 118‐bus system, the WECC 240‐bus test system, the 1354‐bus PEGASE system, and the 2383‐bus Polish winter‐peak test system.