{'fraction_non_alphanumeric': 0.015436565364206465, 'fraction_numerical': 0.000964785335262904, 'mean_word_length': 5.8448844884488445, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Optimal Power Flow in Distribution Networks Under N - 1 Disruptions: A Multistage Stochastic Programming Approach

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.