Fair and Reliable Reconnections for Temporary Disruptions in Electric Distribution Networks using Submodularity

The economic cost of power outages has been estimated to be between \$35 billion and \$50 billion annually in the United States. We analyze and advance methodologies for electrical distribution network reconfiguration in order to quickly restore power, an important lever for improving reliability. For short-term network disruptions, we give a novel model for reconfiguration by considering switches that can be sequentially closed upon detection of a network anomaly upstream. The order in which switches close has an impact on reliability metrics such as SAIDI, which are the basis for regulator-imposed financial performance incentives. We introduce the Minimum Reconnection Time (MRT) problem of finding an optimal switch ordering that minimizes the cost of outages and show that it generalizes metrics like SAIDI. We first show that MRT is a special case of the well-known minimum linear ordering problem from submodular optimization literature and that MRT is also NP-hard. We show how to approximate MRT using recent kernel-based randomized rounding approaches, and in turn improve the state-of-the-art for a broad class of MLOP instances. Finally, we note that the choice of reliability metric can result in significant differences for low and medium voltage buses. We therefore consider optimizing multiple metrics simultaneously using local search methods that reconfigure the system's base tree to optimize service disruptions, reconnection times, and energy losses. We computationally validate our reconfiguration methods on the NREL SMART-DS Greensboro synthetic urban-suburban network and show significant improvement in reliability metrics.